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Any replacements are listed farther down
[196] viXra:2412.0103 [pdf] submitted on 2024-12-17 22:16:18
Authors: Theophilus Agama
Comments: 24 Pages. This is a consolidated work bringing together several pieces into a unified work.
This paper introduces problem theory, a new framework for studying problem and solution spaces through the lens of point-set topology and abstract algebra. We define solution spaces as topological constructs induced by the assignment of solutions to problems and establish their fundamental properties. Key results include the identification of compactness and continuity conditions in solution spaces and their algebraic interpretations within module-theoretic settings. This theory bridges abstract algebra and topology, providing new insights into the interplay between algebraic structures and topological spaces. Potential applications and directions for future research are discussed.
Category: Topology
[195] viXra:2410.0154 [pdf] submitted on 2024-10-25 17:23:04
Authors: Ruohan Yang
Comments: 12 Pages.
This article investigates the two-dimensional Brouwer Fixed-Point Theorem within the context of a surjective continuous transformation function ( f(x) ). This function can be interpreted as defining a continuous vector field. In this framework, each point in the disk is mapped to another point via a specific vector associated with the continuous transformation, thereby establishing a coherent vector field. This function can be interpreted as defining a continuous vector field. In this framework, the vector field can be decomposed two vector fields. Instead of proving the existence of fixed point directly, the article aim to focus on prove the vector fields always has intersection where at this point, the vector fields has opposite directiond and same norm.The paper also provide the programming experiment which further verifies the proof.
Category: Topology
[194] viXra:2410.0153 [pdf] submitted on 2024-10-25 17:21:54
Authors: Ruohan Yang
Comments: 7 Pages.
This article present a constructive proof by analyzing decompositions of continuous vector field. The original proof of Brouwer's theorem relies on a contradiction argument, which, while effective, does not offer a constructive method for locating the fixed point. Through projecting arbitrary vector field the basis of the vector field, it can be proved there exists zero points on both of the basis. The article will also generalize the proof from 2D to 3D dimensions. The method is also valid under surjective and scaling map.
Category: Topology
[193] viXra:2410.0112 [pdf] submitted on 2024-10-19 02:40:00
Authors: Theophilus Agama
Comments: 7 Pages. This paper introduces an analysis on the topology of problem spaces.
We develop the analysis of the theory of problem and their solution spaces. We adapt some classical concepts in functional analysis to study problems and their corresponding solution spaces. We introduce the notion of compactness, density, convexity, boundedness, amenability and the interior. We examine the overall interplay among these concepts in theory.
Category: Topology
[192] viXra:2402.0001 [pdf] submitted on 2024-02-01 00:54:10
Authors: Ryan J. Buchanan
Comments: 12 Pages.
Given a collection of sections of a principal fiber running from the base of a topological space to its top, can we recreate the entire topological space? We answer this question in the affirmative for symplectic manifolds,assuming we are given a filtration of weights. Using the weights which are representative generators at each local neighborhood about each section of a smooth fiber, we reduce our original problem to the Ricci-iterated mapping of Riemann surfaces along a geodesic.
Category: Topology
[191] viXra:2401.0094 [pdf] submitted on 2024-01-21 01:09:06
Authors: Alfonso De Miguel Bueno
Comments: 24 Pages. 22 figures
This paper introduces a fields model based on two intersecting fields varying either same or opposite phase that may graphically illustrate the Jacobian conjecture for four variables. It also suggests the relation of the conjecture with other mathematical topics as Sobolev function spaces interpolation, Reflection positivity, the Mass gap problem, or Tomita-Takesaki modular theory. Being applicable to the Jacobian conjecture, the model would represent a confirmation case in both the symmetric and antisymmetric systems. However, in the symmetric system the mirror reflection property would not be considered by the conjecture when it comes to the vertical subfields.
Category: Topology
[190] viXra:2401.0049 [pdf] submitted on 2024-01-10 11:15:25
Authors: Ryan J. Buchanan
Comments: 12 Pages.
This document is devoted to understanding and implementing the energy numbers, which were recently explicated very clearly by Emmerson in his recent paper. Through this line of reasoning, it becomes apparent that the algebra defined by the energy numbers are indeed the natural algebra for categorifying quantization. We also develop a notion of symmetric topological vector spaces, and forcing on said spaces motivated by homological mirror symmetry.
Category: Topology
[189] viXra:2312.0129 [pdf] submitted on 2023-12-24 20:08:29
Authors: Ryan J. Buchanan
Comments: 18 Pages.
We consider strings from the perspective of stable motivic, homotopical QFT. Some predictions for the behavior of gauginos in both a Minkowski light cone and $5$-dimensional $mathcal{A}dmathcal{S}_5$-space are given. We show that there is a duality between working locking in a system of dendrites, and threshold edging at the periphery of a manifold.This work extends the work of [4] and [7] by providing a more mathematical interpretation of the realization of quasi-quanta in open topological dynamical systems. This interpretation incidentally involves the category of pure motives over $mathfrak{C}$, and projections of fiber spectra to the category of stable homotopies.
Category: Topology
[188] viXra:2312.0113 [pdf] submitted on 2023-12-21 16:18:38
Authors: Ryan J. Buchanan
Comments: 6 Pages.
One of the possible explanations for entanglement is a sort of perverse holonomy which acts on sheaves whose germs are eigenvectors for a tuple of local variables. We take baby steps towards realizing this model by introducing an equivariant form of holonomy. As a test category, we take U(1)-bundles whose outbound fibrations are Koszul nerves of degree (p+q)=n.
Category: Topology
[187] viXra:2310.0128 [pdf] submitted on 2023-10-27 17:02:36
Authors: Ryan J. Buchanan
Comments: 8 Pages.
Let $mathfrak{X}$ be a topological stack, and $LocSys(mathfrak{X})$ a local system taking varieties $v in mathfrak{X}$ to their projective resolutions over an affine coordinate system. Let $alpha$ and $beta$ be smooth charts encompassing non-degenerate loci of the upper-half plane, and let $varphi$ be the map $beta circ alpha^{-1}$. Our goal is to describe a class of vector bundles, called $emph{geometric sub-bundles}$, which provide holonomic transport for n-cells (for small values of n) over a $G_delta$-space which models the passage $mathfrak{X} ightrightarrows LocSys(mathfrak{X})$. We will first establish the preliminary definitions before advancing our core idea, which succinctly states that for a pointed, stratified space $Strat_M^ast$, there is a canonical selection of transition maps $[varphi]$ which preserves the intersection of a countable number of fibers in some sub-bundle of the bundle $Bun_V$ over $LocSys(mathfrak{X})$
Category: Topology
[186] viXra:2307.0083 [pdf] submitted on 2023-07-16 05:57:47
Authors: Ryan J. Buchanan
Comments: 16 Pages.
Let K0,K1 be Kolmogorov spaces, and there be an exact morphism K0 → K1. Assuming K0 to be a "good moduli stack" gives us an exact injection into the category of hyperspace tilings. Here, we explore this link. We supply a healthy dose of background information to get the reader acquainted with the relevant topics in a lightning-round fashion. In the process we touch on automorphisms of spectral sequences.
Category: Topology
[185] viXra:2307.0059 [pdf] submitted on 2023-07-12 21:32:15
Authors: Ryan J. Buchanan
Comments: 13 Pages.
We continue from our last session on ��∞-spaces. Here, we discuss apartments as graphs. Theradial completion of the apartments relate to bundle gerbes and also Mochizuki’s ideas of the ��-link.
Category: Topology
[184] viXra:2307.0003 [pdf] submitted on 2023-07-01 02:14:29
Authors: Ryan J. Buchanan
Comments: 14 Pages.
We introduce here a new notion of polarity for hyperbolic and complex analytic spaces. We describe compasses and arithmetic displays for said spaces.
Category: Topology
[183] viXra:2303.0115 [pdf] submitted on 2023-03-18 21:27:01
Authors: Tianhao Wei, Shucheng Kang, Ruixuan Liu, Changliu Liu
Comments: 7 Pages.
Safety is critical in robotic tasks. Energy function based methods have been introduced to address the problem. To ensure safety in the presence of control limits, we need to design an energy function that results in persistently feasible safe control at all system states.However, designing such an energy function for high-dimensional nonlinear systems remains challenging.Considering the fact that there are redundant dynamics in high dimensional systems with respect to the safety specifications, this paper proposes a novel approach called abstract safe control.We propose a system abstraction method that enables the design of energy functions on a low-dimensional model.Then we can synthesize the energy function with respect to the low-dimensional model to ensure persistent feasibility.The resulting safe controller can be directly transferred to other systems with the same abstraction, e.g., when a robot arm holds different tools. The proposed approach is demonstrated on a 7-DoF robot arm (14 states) both in simulation and real-world. Our method always finds feasible control and achieves zero safety violations in 500 trials on 5 different systems.
Category: Topology
[182] viXra:2208.0133 [pdf] submitted on 2022-08-24 11:43:47
Authors: Eduardo Magalhães
Comments: 20 Pages.
In this paper, I present a generalization of the key notions of limits of sequences and Cauchy sequences from analysis and metric spaces to more general topological groups. In the second part of this paper, the process of constructing the real numbersfrom Cauchy sequences of rationals is generalized, allowing us to construct new groups from non-complete topological groups.
Category: Topology
[181] viXra:2208.0074 [pdf] submitted on 2022-08-12 03:45:37
Authors: Savinov Sergei
Comments: 2 Pages.
The preprint provides a consideration of limiting the lower limit of the chromatic number to 7
Category: Topology
[180] viXra:2207.0115 [pdf] submitted on 2022-07-17 02:10:06
Authors: Thomas Halley
Comments: 13 Pages.
Let k( i^ ) not equal to m. We define an arrow. We show that D = 0. Thompson’s computation of ideals was a milestone in parabolic knot theory. In contrast to [2], a useful suggestion of the subject can be found following Conjecture 6.2 concluding this paper.
Category: Topology
[179] viXra:2207.0068 [pdf] submitted on 2022-07-09 02:47:49
Authors: Sing Kuang Tan
Comments: 9 Pages.
In this paper, we developed a set of linear constraints to test whether 4 points form a square. Traditionally people use Euclidean distance to test whether the 4 points form a square. It forms a square if the four sides are of equal length and the diagonals are of equal length. My test function using a set of linear constraints is much simpler without the use of quadratic operations in Euclidean distance test function. This is needed in the future to prove Square Peg Problem for any arbitary closed curve.
Category: Topology
[178] viXra:2207.0050 [pdf] submitted on 2022-07-06 14:49:33
Authors: Thomas Halley
Comments: 48 Pages.
A basic smooth manifold and a rational smooth set is explored with variations in proving that R is not equal to i.
Category: Topology
[177] viXra:2205.0062 [pdf] submitted on 2022-05-11 14:03:47
Authors: Nikolay Dementev
Comments: 5 Pages.
Method of mapping the knots is suggested. Prospective biological implementations are discussed.
Category: Topology
[176] viXra:2104.0171 [pdf] submitted on 2021-04-27 03:30:33
Authors: Antoine Balan
Comments: 2 pages, written in french
We define a cohomology for the exterior forms over a manifold. It generalizes the De Rham cohomology.
Category: Topology
[175] viXra:2102.0023 [pdf] submitted on 2021-02-04 20:24:20
Authors: Fadhil Hussein Abbas
Comments: 13 Pages. [Corrections made by viXra Admin to conform with scholarly norm]
In this paper, we introduce the notion of intuitionistic fuzzy soft ideal in intuitionistic
fuzzy soft set theory. Also we introduce the concept of intuitionistic fuzzy soft local function. These concepts are discussed with a view to find new intuitionistic fuzzy soft topologies from the original one. The basic structure, especially a basis for such generated intuitionistic fuzzy soft topologies also studied here. The notion of compatibility of intuitionistic fuzzy soft ideals with
intuitionistic fuzzy soft topologies is introduced and some equivalent conditions concerning this
topic are established here. Finally we introduce intuitionistic fuzzy soft-I-open set, intuitionistic fuzzy soft pre-I-open set, intuitionistic fuzzy soft semi-I-open set, intuitionistic fuzzy soft-α-Iopen set and intuitionistic fuzzy soft-β-I-open set and discuss some of their properties.
Category: Topology
[174] viXra:2102.0022 [pdf] submitted on 2021-02-04 20:28:27
Authors: Fadhil Hussein Abbas
Comments: 14 Pages. [Corrections made by viXra Admin to conform with scholarly norm]
In this paper, we introduce a new class of open sets in a topological space (X; τ) called h-open sets. Also, introduce and study topological properties of h-interior, h-closure, h-limit points, h-derived, h-interior points, h-border, h-frontier and h-exterior by using the concept of h-open sets. Moreover introduce the notion of h-continuous functions, h-open functions, h-irresolute functions, h-totally continuous functions, h-contra-continuous functions, h-homeomorphism and investigate some properties of these functions and study some properties, remarks related to them.
Category: Topology
[173] viXra:2102.0021 [pdf] submitted on 2021-02-04 20:30:15
Authors: Fadhil Hussein Abbas
Comments: 11 Pages.
In this paper, we introduce the notion of L-ideal in L-set theory. Also we introduce the concept of L-local function. These concepts are discussed with a view to find new L-topologies from the original one. The basic structure, especially a basis for such generated L-topologies also studied here. The notion of L-compatibility of L-ideals with L-topologies is introduced and some equivalent conditions concerning this topic are established here. Moreover, by using L-local
function we introduce L-operator ψ satisfying ψ(AL) = 1X – (1X – AL)*, for all AL ⊆ LX and we
discuss some characterizations this L-operator by use L-open sets.
Category: Topology
[172] viXra:2101.0113 [pdf] submitted on 2021-01-18 07:07:04
Authors: Pierre-Yves Gaillard
Comments: 4 Pages.
We show that for each topological space X there is a topological space Y such that the quotient space G\Y of Y by the action of the automorphism group G of Y is homeomorphic to X.
Category: Topology
[171] viXra:2101.0005 [pdf] submitted on 2021-01-01 12:21:36
Authors: Arturo Tozzi
Comments: 4 Pages.
Take a balloon, that is a genus-one manifold. If you break the jointness by piercing its surface, the hole gest lost and the punctured balloon becomes a genus-0 manifold. Starting from this trivial claim, we prove a topological theorem which plainly states that “the ends of a donut can meet, whilst the ends of a kidney pie cannot”. In this succinct note, we discuss the theorem and its implications in disparate topics such as topological connectedness, gauge theories and the physics of the black holes.
Category: Topology
[170] viXra:2011.0164 [pdf] submitted on 2020-11-21 17:32:58
Authors: Alexander Chang
Comments: 6 Pages.
Recent advances have begun to blur the lines between theoretical mathematics and applied mathematics. Oftentimes, in a variety of fields, concepts from not only applied mathematics but theoretical mathematics have been employed to great effect. As more and more researchers come to utilize, deploy, and develop both abstract and concrete mathematical models (both theoretical and applied), the demand for highly generalizable, accessible, and versatile mathematical models has increased drastically (Rosen, 2011). Specifically in the case of Complex Systems and the accompanying field of Complex Systems Analysis, this phenomenon has had profound effects. As researchers, academics, and scholars from these fields turn to mathematical models to assist in their scientific inquiries (specifically, concepts and ideas taken from various subsets of graph theory), the limitations of our current mathematical frameworks becomes increasingly apparent. To remedy this, we present the Chang Graph, a simple graph defined by an n-sided regular polygon surrounding a 2n-sided regular polygon. Various properties and applications of this graph are discussed, and further research is proposed for the study of this mathematical model.
Category: Topology
[169] viXra:2011.0043 [pdf] submitted on 2020-11-06 09:04:24
Authors: Yu-Lin Chou
Comments: 3 Pages. expository article
That every Euclidean subset homeomorphic to the ambient Euclidean space is open, a version of invariance of domain, is a relatively deep result whose typical proof is far from elementary. When it comes to the real line, the version of invariance of domain admits a simple proof that depends precisely on some elementary results of ``common sense''. It seems a pity that an elementary proof of the version of invariance of domain for the real line is not well-documented in the related literature even as an exercise, and it certainly deserves a space. Apart from the main purpose, as we develop the ideas we also make present some pedagogically enlightening remarks, which may or may not be well-documented.
Category: Topology
[168] viXra:2011.0042 [pdf] submitted on 2020-11-06 08:47:36
Authors: Yu-Lin Chou
Comments: 4 Pages. expository article
We wish to demystify the concept of a homeomorphism for anyone who finds the idea ``intangible'', by showing that one can construct a homeomorphism out of any given bijection in a natural way. Some interdisciplinary examples are discussed for concreteness.
Category: Topology
[167] viXra:2009.0150 [pdf] submitted on 2020-09-21 20:09:28
Authors: Eduardo Magalhães
Comments: 1 Page.
This short note presents a very simple and intuitive counterexample that disproves the statement “If (X,τ) is a topological space with the finite-closed topology, then it has the fixed-point property”.
Category: Topology
[166] viXra:2007.0208 [pdf] submitted on 2020-07-27 09:11:03
Authors: Jorma Jormakka
Comments: 14 Pages. This is a rewritten and carefully checked version of my 2011 paper.
The paper presents a counterexample to the Hodge conjecture.
Category: Topology
[165] viXra:2007.0113 [pdf] submitted on 2020-07-15 01:07:12
Authors: Dmitri Martila
Comments: 8 Pages. Rejected by many top journals without review
Besides the proof of the mathematical conjecture, a new form for the three-dimensional euclidean sphere is given. This sphere can be embedded
into pseudo-euclidean metric, making the new description for the Universe.
Category: Topology
[164] viXra:2005.0273 [pdf] submitted on 2020-05-28 16:20:35
Authors: Giorgio Nordo
Comments: 10 Pages.
In this paper we generalize the notion of perfect compactification of a Tychonoff space to a generic extension of any space by introducing the concept of perfect pair. This allow us to simplify the treatment in a basic way and in a more general setting. Some Skljarenko and Diamond’s results are improved and new characterizations for perfect (Hausdorff) extensions of spaces are obtained.
Category: Topology
[163] viXra:2005.0272 [pdf] submitted on 2020-05-28 16:22:50
Authors: Giorgio Nordo
Comments: 11 Pages.
We present some recent results in Fibrewise General Topology (FGT) with special regard to the theory of Tychonoff compactifications of mappings. Several open problems are also proposed.
Category: Topology
[162] viXra:2005.0266 [pdf] submitted on 2020-05-28 10:16:11
Authors: Giorgio Nordo, Arif Mehmood, Said Broumi
Comments: 14 Pages.
In this paper we give a comprehensive presentation of the notions of filter base, filter and ultrafilter on single valued neutrosophic set and we investigate some of their properties and relationships. More precisely, we discuss properties related to filter completion, the image of neutrosophic filter base by a neutrosophic induced mapping and the infimum and supremum of two neutrosophic filter bases.
Category: Topology
[161] viXra:2004.0217 [pdf] submitted on 2020-04-09 17:07:42
Authors: Giorgio NORDO
Comments: 7 Pages.
In 1999, Molodtsov initiated the concept of Soft Sets Theory as a new mathematical tool and a completely different approach for dealing with uncertainties in many fields of applied sciences. In 2011, Shabir and Naz introduced and studied the theory of soft topological spaces, also defining and investigating many new soft properties as generalization of the classical ones. In this paper, we introduce the notions of soft separation between soft points and soft closed sets in order to obtain a generalization of the well-known Embedding Lemma for soft topological spaces.
Category: Topology
[160] viXra:2003.0426 [pdf] submitted on 2020-03-20 18:30:58
Authors: Vincenzo Nardozza
Comments: 2 Pages.
We introduce the idea of an Essential Spaces for 2-dimensional compact manifolds. We raise the question whether essential spaces do exist also for 3-dimensional manifolds.
Category: Topology
[159] viXra:2002.0481 [pdf] submitted on 2020-02-24 21:56:43
Authors: P. Karthiksankar
Comments: 6 Pages.
The aim of this paper is to introduce the concepts of IFS α -open sets.
Also we discussed the relationship between this type of Open set and
other existing Open sets in Intuitionistic fuzzy topological spaces. Also
we introduce new class of closed sets namely IFS α -closed sets and its
properties are studied.
Category: Topology
[158] viXra:2002.0229 [pdf] submitted on 2020-02-12 06:26:06
Authors: Dmitry Vatolin
Comments: 2 Pages.
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Category: Topology
[157] viXra:2001.0647 [pdf] submitted on 2020-01-29 14:27:06
Authors: Miguel Caldas, Saeid Jafari, Takashi Noiri
Comments: 12 Pages.
In this paper we introduce two new classes of topological spaces called pre-R0 and pre-R1 spaces in terms of the concept of preopen sets and investigate some of their fundamental properties.
Category: Topology
[156] viXra:2001.0645 [pdf] submitted on 2020-01-29 14:31:23
Authors: C. W. Baker, M. Caldas, Saeid Jafari, S. P. Moshokoa
Comments: 14 Pages.
In 1996, Dontchev [14] introduced and investigated a new notion of non-continuity called contra-continuity. Recently, Baker et al. [6] of-
fered a new generalization of contra-continuous functions via $\lambda$-closed
sets, called almost contra $\lambda$-continuous functions. It is the objective
of this paper to further study some more properties of such functions.
Category: Topology
[155] viXra:2001.0644 [pdf] submitted on 2020-01-29 14:34:55
Authors: M. Caldas, Saeid Jafari
Comments: 10 Pages.
The purpose of this paper is to introduce some new classes of topological spaces by utilizing b-open sets and study some of their fundamental properties
Category: Topology
[154] viXra:2001.0643 [pdf] submitted on 2020-01-29 14:43:00
Authors: C. W. Baker, M. Caldas, Saeid Jafari
Comments: 9 Pages.
In the present paper, we offer a new form of firm continuity, called firm contra-continuity, by which we characterize strongly S-closed spaces. Moreover, we investigate the basic properties of firmly contra-continuous functions. We also introduce and
investigate the notion of locally contra-closed graphs.
Category: Topology
[153] viXra:2001.0642 [pdf] submitted on 2020-01-29 14:46:23
Authors: M. Caldas, Saeid Jafari, R. M. Latif, T. Noiri
Comments: 12 Pages.
In this paper, we study some properties of functions with strongly $\alpha$-closed graphs by utilizing $\alpha$-open sets and the $\alpha$-closure operator.
Category: Topology
[152] viXra:2001.0641 [pdf] submitted on 2020-01-29 14:51:56
Authors: M. Caldas, M. Ganster, D. N. Georgiou, Saeid Jafari
Comments: 16 Pages.
It is the object of this paper to study further the notion of $\Lambda s$-semi-
$\theta$-closed sets which is defined as the intersection of a $\theta$- $\Lambda s$-set and a
semi--closed set. Moreover, we introduce some low separation axioms using the above notions. Also we present and study the notions of $\Lambda s$-
continuous functions, $\Lambda s$-compact spaces and $\Lambda s$-connected spaces.
Category: Topology
[151] viXra:2001.0640 [pdf] submitted on 2020-01-29 14:55:30
Authors: M. Caldas, M. Ganster, Saeid Jafari, T. Noiri
Comments: 12 Pages.
M. Ganster and I.L. Reilly [2] introduced a new decomposition of continuity called LC-continuity. In this paper, we introduce and investigate a generalization LC- continuity called weakly LC-continuity.
Category: Topology
[150] viXra:2001.0638 [pdf] submitted on 2020-01-29 15:00:19
Authors: S.P. Missier, M.G. Rani, M. Caldas, Saeid Jafari
Comments: 11 Pages.
In this paper, we introduce a new class of continuous functions as an application
of $\Lambda$-generalized closed sets (namely $\Lambda_g$-closed set, $\Lambda$-g-closed set and $g \Lambda$-closed set)
namely $\Lambda$-generalized continuous functions (namely $\Lambda g$-continuous, $\Lambda$-g-continuous and $g \Lambda$-continuous) and study their properties in topological space.
Category: Topology
[149] viXra:2001.0637 [pdf] submitted on 2020-01-29 15:02:50
Authors: Maximilian Ganster, Saeid Jafari
Comments: 6 Pages.
Recently the notion of rarely $\alpha$-continuous functions has been introduced and investigated
by Jafari [1]. This paper is devoted to the study of upper (and lower) rarely $\alpha$-continuous multifunctions.
Category: Topology
[148] viXra:2001.0635 [pdf] submitted on 2020-01-29 15:26:36
Authors: M. Caldas, Saeid Jafari, T. Noiri, R.K. Saraf
Comments: 12 Pages.
In this note, we study some other properties of functions with strongly semi-$\theta$-closed graphs by utilizing semi-$\theta$--open sets and the
semi-$\theta$--closure operator.
Category: Topology
[147] viXra:2001.0581 [pdf] submitted on 2020-01-27 00:56:28
Authors: Esref Hatir, Saeid Jafari
Comments: 8 Pages.
In this paper, we present and study some new classes of sets and give a new decomposition of continuity in terms of grills.
Category: Topology
[146] viXra:2001.0561 [pdf] submitted on 2020-01-26 08:03:37
Authors: S.P. Missier, M.G. Rani, M. Caldas, Saeid Jafari
Comments: 20 Pages.
In this paper, we first introduce a new class of closed map called $\rho$-
closed map. Moreover, we introduce a new class of homeomorphism called
a $\rho$-homeomorphism.We also introduce another new class of closed map
called $\rho*$-closed map and introduce a new class of homeomorphism called
a $\rho*$-homeomorphism and prove that the set of all $\rho*$-homeomorphisms
forms a group under the operation of composition of maps.
Category: Topology
[145] viXra:2001.0560 [pdf] submitted on 2020-01-26 08:11:15
Authors: M. Anto, K. M. Arifmohammed, M. Ganster, Saeid Jafari, S. Pious Missier
Comments: 29 Pages.
In this paper, we introduce kT½ -spaces, k*T½ -spaces, kT_b -spaces, kT_c -spaces,
kT_d -spaces, kT_f -spaces, kT_^g* -spaces and T^k_b-spaces and investigate their characterizations.
Category: Topology
[144] viXra:2001.0542 [pdf] submitted on 2020-01-25 06:38:43
Authors: M. Caldas, Saeid Jafari, T. Noiri
Comments: 10 Pages.
In this paper we define the concept of $\Lambda_b$-sets (resp. $V_b$-sets) of a topological space,
i.e., the intersection of b-open (resp. the union of b-closed) sets. We study the fundamental
property of $\Lambda_b$-sets (resp. $V_b$-sets) and investigate the topologies defined by
these families of sets.
Category: Topology
[143] viXra:2001.0541 [pdf] submitted on 2020-01-25 06:43:12
Authors: R. Dhavaseelan, Saeid Jafari, F. Smarandache
Comments: 4 Pages.
The concept of neutrosophic locally compact and neutrosophic compact open topology are introduced and some interesting propositions are discussed.
Category: Topology
[142] viXra:2001.0540 [pdf] submitted on 2020-01-25 06:49:07
Authors: M. Ganster, Saeid Jafari, M. Steiner
Comments: 9 Pages.
The aim of this paper is to consider compactness notions by utilizing $\lambda$-sets, V -
sets, locally closed sets, locally open sets, $\lambda$-closed sets and $\lambda$-open sets. We are able to completely characterize these variations of compactness, and also provide various
interesting examples that support our results.
Category: Topology
[141] viXra:2001.0539 [pdf] submitted on 2020-01-25 06:51:58
Authors: M. Ganster, Saeid Jafari, T. Noiri
Comments: 10 Pages.
In this paper we consider a new class of topological spaces, called pc-compact spaces.
This class of spaces lies strictly between the classes of strongly compact spaces and C-
compact spaces. Also, every pc-compact space is p-closed in the sense of Abo-Khadra.
We will investigate the fundamental properties of pc-compact spaces, and consider their
behaviour under certain mappings.
Category: Topology
[140] viXra:2001.0538 [pdf] submitted on 2020-01-25 06:56:53
Authors: Miguel Caldas, Saeid Jafari, Raja M. Latif, Oya B. Özbakir
Comments: 10 Pages.
Balachandran [1] introduced the notion of GO-compactness by involving g-open
sets. Quite recently, Caldas et al. in [8] and [9] investigated this class of compactness
and characterized several of its properties. In this paper, we further investigate this
class of compactness and obtain several more new properties. Moreover, we introduce
and study the new class of GO-(m, n)-compact spaces.
Category: Topology
[139] viXra:2001.0537 [pdf] submitted on 2020-01-25 07:02:20
Authors: Saeid Jafari, N. Rajesh
Comments: 11 Pages.
In this paper, we introduce and study the class of ideal topological groups by using I-open sets and I-continuity.
Category: Topology
[138] viXra:2001.0535 [pdf] submitted on 2020-01-25 07:10:02
Authors: Saeid Jafari, N. Rajesh, F. Smarandache
Comments: 9 Pages.
This paper is devoted to the concepts of neutrosophic upper and neutrosophic lower contra-continuous multifunctions and also some of their characterizations are considered.
Category: Topology
[137] viXra:2001.0534 [pdf] submitted on 2020-01-25 07:12:43
Authors: R. Dhavaseelan, Saeid Jafari, N. Rajesh, F. Smarandache
Comments: 10 Pages.
In this paper we introduce the concepts of neutrosophic upper and neutrosophic lower semi-continuous multifunctions and study some of their basic properties.
Category: Topology
[136] viXra:2001.0518 [pdf] submitted on 2020-01-24 02:05:43
Authors: Volker Thürey
Comments: 37 Pages.
We generalize the very well known boundary operator of the ordinary singular homology theory.
We describe a variant of this ordinary simplicial boundary operator, where the usual boundary (n-1)-simplices of each n-simplex, i.e. the `faces´, are replaced by combinations of internal (n-1)-simplices parallel to the faces. This construction may lead to an infinte class of extraordinary non-isomorphic homology theories.
Further, we show some interesting constructions on the standard simplex.
Category: Topology
[135] viXra:2001.0483 [pdf] submitted on 2020-01-22 13:07:32
Authors: E. Ekici, Saeid Jafari
Comments: 7 Pages.
The aim of this paper is to present a new class of complete irresoluteness. The notion of completely $\delta$-semi-irresolute functions is introduced and studied.
Category: Topology
[134] viXra:2001.0482 [pdf] submitted on 2020-01-22 13:09:39
Authors: E. Ekici, Saeid Jafari
Comments: 10 Pages.
The main purpose of this paper is to introduce the notions of D-sets, DS-sets, D-continuity and DS-continuity and to obtain decompositions of continuous functions, A-continuous functions and AB-continuous functions. Also, properties of the
classes of D-sets and DS-sets are discussed.
Category: Topology
[133] viXra:2001.0481 [pdf] submitted on 2020-01-22 13:21:44
Authors: E. Ekici, Saeid Jafari
Comments: 9 Pages.
In this paper, the notions of DS*-sets and DS*-continuous functions are introduced and their properties and their relationships with
some other types of sets are investigated. Moreover, some new decompositions of continuous functions are obtained by using DS*-continuous
functions, DS-continuous functions and D-continuous functions.
Category: Topology
[132] viXra:2001.0480 [pdf] submitted on 2020-01-22 13:26:53
Authors: E. Ekici, Saeid Jafari, R. M. Latif
Comments: 13 Pages.
In 1943, Fomin [7] introduced the notion of θ-continuity. In 1966, the notions of θ-open subsets, θ-closed subsets and θ-closure were introduced by Veliˇcko [18] for the purpose of studying the important class of H-closed spaces in terms of arbitrary filterbases. He also showed
that the collection of θ-open sets in a topological space (X, τ ) forms
a topology on X denoted by τ θ (see also [12]). Dickman and Porter
[4], [5], Joseph [11] continued the work of Veliˇcko. Noiri and Jafari
[15], Caldas et al. [1] and [2], Steiner [16] and Cao et al [3] have also
obtained several new and interesting results related to these sets. In this paper, we will offer a finer topology on X than $\tau_\theta$ by utilizing the new notions of ωθ-open and ωθ-closed sets. We will also discuss some of the fundamental properties of such sets and some related maps.
Category: Topology
[131] viXra:2001.0479 [pdf] submitted on 2020-01-22 13:48:09
Authors: M. Caldas, Saeid Jafari, K.Viswanathan, S.Krishnaprakash
Comments: 10 Pages.
In this paper, we introduce and investigate the notion of contra $\pigp$-continuous functions by
utilizing Park’s $\pigp$− closed sets [18]. We obtain fundamental properties of contra $\pigp$-continuous functions and discuss the relationships between contra $\pigp$-continuity and other related functions.
Category: Topology
[130] viXra:2001.0478 [pdf] submitted on 2020-01-22 13:50:25
Authors: M. Alimohammady, E. Ekici, Saeid Jafari, M. Roohi
Comments: 11 Pages.
This paper is devoted to the concepts of fuzzy upper and fuzzy lower contra-continuous multifunctions and also some characterizations of them are considered.
Category: Topology
[129] viXra:2001.0477 [pdf] submitted on 2020-01-22 13:53:01
Authors: M. Alimohammady, E. Ekici, Saeid Jafari, M. Roohi
Comments: 8 Pages.
In this paper, we deal with some separation axioms in the context of fuzzy minimal structures.
Category: Topology
[128] viXra:2001.0436 [pdf] submitted on 2020-01-21 16:45:41
Authors: M. Caldas, E. Ekici, Saeid Jafari
Comments: 6 Pages.
In this paper, we o®er the new notion of preseparatedness in topological spaces and we study some of its fundamental properties.
Category: Topology
[127] viXra:2001.0412 [pdf] submitted on 2020-01-20 16:40:58
Authors: Saeid Jafari
Comments: 8 Pages.
In this paper, we deal with the new class of pre-regular p-open sets in which the notion
of preopen set is involved. We characterize these sets and study some of their fundamental
properties. We also present two other notions called extremally $p$-discreteness and locally $p$-indiscreteness by utilizing the notions of preopen and preclosed sets by which we obtain some equivalence relations for pre-regular p-open sets. Moreover, we define the notion of regular $p$-open sets by utilizing the notion of pre-regular p-open sets. We investigate some of the main
properties of these sets and study their relations to pre-regular $p$-open sets.
Category: Topology
[126] viXra:2001.0411 [pdf] submitted on 2020-01-20 16:59:18
Authors: Alias B. Khalaf, Saeid Jafari, Hariwan Z. Ibrahim
Comments: 15 Pages.
In this paper, we consider the class of $\alpha_{[\gamma, \gamma']}generalized
closed set in topological spaces and investigate some of their properties.
We also present and study new separation axioms by using the notions of $\alpha$-open and $\alpha$-bioperations. Also, we analyze the relations with some well known separation axioms.
Category: Topology
[125] viXra:2001.0410 [pdf] submitted on 2020-01-20 17:03:09
Authors: Alias B. Khalaf, Suzan N. Dawod, Saeid Jafari
Comments: 19 Pages.
In this paper we introduce new types of functions called g*bp-continuous function, almost g*bp-continuous function, and weakly g*bp-continuous function in topological spaces and study some of their basic properties and relations among them.
Category: Topology
[124] viXra:2001.0409 [pdf] submitted on 2020-01-20 17:06:58
Authors: Mohsen Alimohammady, Saeid Jafari, Seithuti P. Moshokoa, Morteza Koozehgar Kalleji
Comments: 12 Pages.
The note studies further properties and results of analysis in the setting of hypermetric spaces. Among others, we present some results concerning the hyper uniform limit of a sequence of continuous functions, the hypermetric identication theorem and
the metrization problem for hypermetric space.
Category: Topology
[123] viXra:2001.0408 [pdf] submitted on 2020-01-20 17:13:57
Authors: Wadei Al-Omeri, Saeid Jafari
Comments: 12 Pages.
In this paper, the concept of generalized neutrosophic pre-closed sets and generalized
neutrosophic pre-open sets are introduced. We also study relations and various properties between the other existing neutrosophic open and closed sets. In addition, we discuss some applications of generalized neutrosophic pre-closed sets, namely neutrosophic pT_{1/2} space and neutrosophic gpT_{1/2} space. The concepts of generalized neutrosophic connected spaces, generalized neutrosophic compact spaces and generalized neutrosophic extremally disconnected spaces are established. Some interesting properties are investigated in addition to giving some examples.
Category: Topology
[122] viXra:2001.0406 [pdf] submitted on 2020-01-20 17:23:28
Authors: A.Arokia Lancy, I. Arockiarani, Saeid Jafari
Comments: 9 Pages.
The purpose of this paper is to introduce some generalized closed sets of general topology to soft interval valued intuitionistic fuzzy topology. In particular the soft interval valued intuitionistic fuzzy semi-pre generalized closed sets along with its characterization are discussed.
Category: Topology
[121] viXra:2001.0405 [pdf] submitted on 2020-01-20 17:26:53
Authors: H. Jude Immaculate, Saeid Jafari, I.Arockiarani
Comments: 10 Pages.
In this paper, we initiate the concept of intuitionistic fuzzy ideals on rough sets. Using a new relation we discuss some of the algebraic nature of intuitionistic fuzzy ideals of a ring.
Category: Topology
[120] viXra:2001.0397 [pdf] submitted on 2020-01-20 06:26:00
Authors: Saeid Jafari, A. Sevakumar, M. Parimala
Comments: 5 Pages.
In this article we introduce $(I; \gamma)$
-$g\star$-closed sets in topological spaces and
also introduce $\gamma g\star$-$T_I$-spaces and investigate some of their properties.
Category: Topology
[119] viXra:2001.0396 [pdf] submitted on 2020-01-20 06:30:01
Authors: M. Caldas, Saeid Jafari
Comments: 18 Pages.
The aim of this paper is to present and study a new type of regularity and normality
called $\beta \theta$-regularity and $\beta \theta$-normality, repectively by using $\beta \theta$-open sets.
Category: Topology
[118] viXra:2001.0395 [pdf] submitted on 2020-01-20 06:34:28
Authors: M. Caldas, Saeid Jafari, T. Noiri
Comments: 17 Pages.
In this paper we consider the class of $\beta \theta$-open sets in topological spaces and investigate
some of their properties. We also present and study some weak separation
axioms by involving the notion of $\beta \theta$-open sets.
Category: Topology
[117] viXra:2001.0394 [pdf] submitted on 2020-01-20 06:40:49
Authors: Saeid Jafari, A. Selvakumar
Comments: 16 Pages.
In this paper , we will continue the study of related irresolute functions with $G \~$ \alpha$-open sets [6]. We introduce and study the notion of completely $G \~$ \alpha$-irresolute functions.
Further, we discuss the notion of $G \~$ \alpha$-quotient functions and study some of their
properties.
Category: Topology
[116] viXra:2001.0393 [pdf] submitted on 2020-01-20 06:45:34
Authors: Saeid Jafari, M. Parimala
Comments: 14 Pages.
The purpose of this paper is to introduce a new type of open sets called mI-open
sets and quasi-$mI$-open sets in minimal ideal topological spaces and investigate the
relation between minimal structure space and minimal ideal structure spaces. Basic
properties and characterizations related to these sets are given.
Category: Topology
[115] viXra:2001.0392 [pdf] submitted on 2020-01-20 06:49:56
Authors: Saeid Jafari, A. Selvakumar
Comments: 15 Pages.
R.Devi et al. [4] introduced the concept of $g\~$$\alpha$-open sets. In this paper, we introduce
and study some properties of functions with ultra $g\~$$\alpha$-closed graphs and strongly
$g\~$$\alpha$-closed graphs by utilizing $g\~$$\alpha$-open sets and the eg-closure operator.
Category: Topology
[114] viXra:2001.0391 [pdf] submitted on 2020-01-20 06:53:57
Authors: Saeid Jafari, A. Selvakumar
Comments: 20 Pages.
The concept of $g\~$$\alpha$-closed sets in a topological space are introduced by R. Devi et.
al. [4]. In this paper, we introduce the notion of contra $g\~$$\alpha$-continuous functions
utilizing $g\~$$\alpha$-open sets and study some of its applications.
Category: Topology
[113] viXra:2001.0390 [pdf] submitted on 2020-01-20 06:59:47
Authors: A. Selvakumar, Saeid Jafari
Comments: 19 Pages.
In this paper, we introduce the notion of $I_{g~\alpha}$ -closed sets in ideal topological spaces and
investigate some of their properties. Further, we introduce the concept of mildly $I_{g~\alpha}$-
closed sets and $I_{g~\alpha}$-normal space.
Category: Topology
[112] viXra:2001.0388 [pdf] submitted on 2020-01-20 07:03:27
Authors: A. Selvakumar, Saeid Jafari
Comments: 10 Pages.
The basic objective of this paper is to introduce and investigate the properties of Nano $g\~$$\alpha$-closed sets in Nano topological spaces.
Category: Topology
[111] viXra:2001.0386 [pdf] submitted on 2020-01-20 07:11:43
Authors: A. Selvakumar, Saeid Jafari
Comments: 7 Pages.
In this paper, we define the $g\~$$\alpha$($\theta$)-convergence and $g\~$$\alpha$($\theta$)-adherence
using the concept of grills and study some of their properties.
Category: Topology
[110] viXra:2001.0385 [pdf] submitted on 2020-01-20 07:14:38
Authors: R. Devi, A. Selvakumar, Saeid Jafari
Comments: 9 Pages.
In this paper, we introduce the notion of $g\~$$\alpha$-closed sets in topological
spaces and investigate some of their basic properties.
Category: Topology
[109] viXra:2001.0383 [pdf] submitted on 2020-01-20 07:19:09
Authors: M. Caldas, Saeid Jafari, T. Noiri, M. S. Sarsak
Comments: 19 Pages.
In this paper, we obtain new separation axioms by
using the notion of $(\delta; p)$-open sets introduced by Jafari [3] via the
notion of pre-regular $p$-open sets [2].
Category: Topology
[108] viXra:2001.0382 [pdf] submitted on 2020-01-20 07:26:21
Authors: M. Vigneshwaran1, Saeid Jafari, S. E. Han
Comments: 19 Pages.
Digital topology was first studied in the late 1970’s by the computer analysis researcher Azriel Rosenfeld [15]. In this paper we derive some of the properties of **gα-open and **gα-closed sets in the digital plane. Moreover, we show that the Khalimsky line $(Z^{2}, K^{2})$ is not an αT_1/2*** space. Also we prove that the family of all **gα-open sets of $(Z^2, K^2)$, say $**GαO(Z^2, K^2)$, forms an alternative topology of Z2 and the topological space (Z2, $**G\alpha O(Z^2, K^2))$ is a T_1/2 space. Moreover, we derive the properties of *gα-closed and *gα-open sets in the digital plane via the singleton’s points
Category: Topology
[107] viXra:2001.0381 [pdf] submitted on 2020-01-20 07:31:08
Authors: S. Saranya, M. Vigneshwaran, Saeid Jafari
Comments: 12 Pages.
In this paper, we have developed a C# application for finding the values of the complement, union, intersection and the inclusion of any two neutrosophic sets in the neutrosophic field by using .NET Framework, Microsoft Visual Studio and C# Programming Language. In addition to this, the system can find neutrosophic topology ($\tau$ ), neutrosophic $g \alpha$-closed sets and neutrosophic $g \alpha$-closed sets in each resultant screens. Also this computer based application produces the complement values of each neutrosophic closed sets.
Category: Topology
[106] viXra:2001.0373 [pdf] submitted on 2020-01-19 17:17:51
Authors: C. Özel, P. Linker, M. Al Shumrani, Saeid Jafari
Comments: 4 Pages.
In this note, we are intended to offer some theoretical consideration concerning the introduction of point-free topological monoids on the locales and frames. Moreover, we define a quantum group on locales by
utilizing the Drinfeld-Jimbo group.
Category: Topology
[105] viXra:2001.0352 [pdf] submitted on 2020-01-18 18:45:19
Authors: Vincenzo Nardozza
Comments: 3 Pages.
In this paper we find and discuss the Strip Configuration of the Poincare' Sphere.
Category: Topology
[104] viXra:2001.0311 [pdf] submitted on 2020-01-16 17:12:53
Authors: M. Parimala, Saeid Jafari
Comments: 9 Pages.
The purpose of this paper is to introduce the notion of nano ideal topological spaces and
investigate the relation between nano topological space and nano ideal topological space. Moreover, we offer some new open and closed sets in the context of nano ideal topological spaces and present some of their basic properties and characterizations.
Category: Topology
[103] viXra:2001.0290 [pdf] submitted on 2020-01-15 13:18:40
Authors: M. Caldas, M. Ganster, Saeid Jafari, T. Noiri, V. Popa, N. Rajesh
Comments: 11 Pages.
The aim of this paper is to introduce and characterize the concepts of
preopen sets and their related notions in ideal generalized topological spaces.
Category: Topology
[102] viXra:2001.0289 [pdf] submitted on 2020-01-15 13:24:57
Authors: M. Caldas, Saeid Jafari, N. Rajesh, F. Smarandache
Comments: 12 Pages.
The aim of this paper is to introduce and character-
ize the concepts of I-open sets and their related notions in ideal
bitopological spaces.
Category: Topology
[101] viXra:2001.0288 [pdf] submitted on 2020-01-15 13:30:32
Authors: M. Caldas, Saeid Jafari, V. Popa, N. Rajesh
Comments: 10 Pages.
The purpose of this paper is to introduce and study the notions $I-R_0$, $I-R_1$, $I-T_0$,
$I-T_1$ and $I-T_2$ in ideal bitopological space.
Category: Topology
[100] viXra:2001.0287 [pdf] submitted on 2020-01-15 13:36:07
Authors: M. Caldas, M. Ganster, Saeid Jafari, T. Noiri, N. Rajesh
Comments: 17 Pages.
The purpose of this paper is to introduce and characterize
the concept of $\alpha$-open set and several related notions in ideal minimal
spaces.
Category: Topology
[99] viXra:2001.0286 [pdf] submitted on 2020-01-15 13:39:34
Authors: Saeid Jafari, T. Noiri, N. Rajesh, R. Saranya
Comments: 9 Pages.
In this paper, we introduce and study the class of
$\beta$-open sets and other related classes of notions in ideal minimal
spaces.
Category: Topology
[98] viXra:2001.0285 [pdf] submitted on 2020-01-15 13:43:48
Authors: Saeid Jafari, N. Rajesh
Comments: 10 Pages.
In this paper, we introduce and study upper and lower slightly $\delta$-$\beta$-
continuous multifunctions in topological spaces and obtain some characterizations
of these new continuous multifunctions.
Category: Topology
[97] viXra:2001.0284 [pdf] submitted on 2020-01-15 13:47:34
Authors: A. I. El-Maghrabi, M. Caldas, Saeid JAFARI, R. M. Latif, A. Nasef, N. Rajesh, S. Shanthi
Comments: 19 Pages.
The aim of this paper is to introduced and character-
ized the concepts of $\alpha$-open sets and their related notions in ideal
bitopological spaces.
Category: Topology
[96] viXra:2001.0283 [pdf] submitted on 2020-01-15 13:53:33
Authors: N. Rajesh, E. Ekici, Saeid Jafari
Comments: 9 Pages.
The purpose of this paper is to introduce the notions
$\¨g-R_0$, $\¨g-R_1$, $\¨g-T_0$, $\¨g-T_1$ and \¨g-T_2$ in bitopological space.
Category: Topology
[95] viXra:2001.0282 [pdf] submitted on 2020-01-15 13:55:44
Authors: Saeid Jafari, N. Rajesh
Comments: 10 Pages.
In this paper, we introduce and study the concept of
qI-open set. Based on this new concept, we dene new classes of
functions, namely qI-continuous functions, qI-open functions and qI-
closed functions, for which we prove characterization theorems.
Category: Topology
[94] viXra:2001.0281 [pdf] submitted on 2020-01-15 13:58:00
Authors: M. Caldas, Saeid Jafari, N. Rajesh
Comments: 16 Pages.
The aim of this paper is to introduced and charac-
terized the concepts of semiopen sets and their related notions in ideal bitopological spaces.
Category: Topology
[93] viXra:2001.0280 [pdf] submitted on 2020-01-15 14:04:05
Authors: Saeid Jafari, S. Shanthi, N. Rajesh
Comments: 5 Pages.
The purpose of this paper is to introduce some new classes of ideal topological spaces by utilizing I-open sets and study some of their fundamental properties.
Category: Topology
[92] viXra:2001.0279 [pdf] submitted on 2020-01-15 14:07:02
Authors: M. Caldas, Saeid Jafari, N. Rajesh
Comments: 9 Pages.
In this paper we introduce and characterize the concepts of $\beta$-open sets and their related
notions in ideal bitopological spaces.
Category: Topology
[91] viXra:2001.0278 [pdf] submitted on 2020-01-15 14:11:39
Authors: Saeid Jafari, N. Rajesh, R. Saranya
Comments: 16 Pages.
In this paper, we present and study the concepts of
semiopen sets and their related notions in ideal minimal spaces.
Category: Topology
[90] viXra:2001.0275 [pdf] submitted on 2020-01-14 21:28:20
Authors: Saeid Jafari, T. Noiri, N. Rajesh
Comments: 9 Pages.
The aim of this paper is to introduce and characterize the concepts of I-open sets and their related notions in ideal minimal spaces.
Category: Topology
[89] viXra:2001.0161 [pdf] submitted on 2020-01-09 14:45:39
Authors: Theophilus Agama
Comments: 11 Pages.
In this paper we introduce and develop the topology of compression of points in space. We then use this Topology to solve the Erd\'{o}s-Ulam problem. We provide a positive solution in this paper.
Category: Topology
[88] viXra:2001.0094 [pdf] submitted on 2020-01-06 16:13:55
Authors: S. Pious Missier, K. M. Arifmohammed, S. Jafari, M. Ganster, A. Robert
Comments: 24 Pages.
The Khalimsky topology plays a significant role in the digital image processing. In this paper we define a topology $\kappa_1$ on the set of integers generated by the triplets of the form $\{2n, 2n+1, 2n+3\}$. We show that in this space $(\mathbb{Z}, \kappa_1)$, every point has a smallest neighborhood and hence this is an Alexandroff space. This topology is homeomorphic to Khalimskt topology. We prove, among others, that this space is connected and $T_{3/4}$. Moreover, we introduce the concept of $^*g\hat{\alpha}$-closed sets in a topological space and characterize it using $^*g\alpha o$-kernel and closure. We investigate the properties of $^*g\hat{\alpha}$-closed sets in digital plane. The family of all $^*g\hat{\alpha}$-open sets of $(\mathbb{Z}^2, \kappa^2)$, forms an alternative topology of $\mathbb{Z}^2$. We prove that this plane $(\mathbb{Z}^2, ^*g\hat{\alpha}O)$ is $T_{1/2}$. It is well known that the digital plane $(\mathbb{Z}^2, \kappa^2)$ is not $T_{1/2}$, even if $(\mathbb{Z}, \kappa)$ is $T_{1/2}$.
Category: Topology
[87] viXra:2001.0092 [pdf] submitted on 2020-01-06 16:24:27
Authors: Sang-Eon Han, Saeid Jafari, Jeong Min Kang
Comments: 12 Pages.
The present paper deals with two types of topologies on the set of integers, Z: a
quasi-discrete topology and a topology satisfying the T½
-separation axiom. Furthermore, for each
$n \in N$, we develop countably many topologies on Zn which are not homeomorphic to the typical
n-dimensional Khalimsky topological space. Based on these different types of new topological
structures on $Z^{n}$, many new mathematical approaches can be done in the fields of pure and applied
sciences, such as fixed point theory, rough set theory, and so on.
Category: Topology
[86] viXra:1912.0352 [pdf] submitted on 2019-12-18 08:45:02
Authors: Dmitri Martila
Comments: 4 Pages.
On December 22, 2006, the journal Science honored Perelman's proof of the Poincare Conjecture as the scientific ``Breakthrough of the Year", the first time this honor was bestowed in the area of mathematics. However, I have critical questions about Perelman's proof of Poincare Conjecture. The conjecture states, that ``Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.'' The ``homeomorphic" means that by non-singular deformation one produces perfect sphere - the equivalent of initial space. However, pasting in foreign caps will not make such deformation. My short proofs are given.
Category: Topology
[85] viXra:1912.0161 [pdf] submitted on 2019-12-08 13:53:21
Authors: Vincenzo Nardozza
Comments: 12 Pages.
We introduce the idea of Solid Strip Configurations which is a way of describing 3-dimensional compact manifolds alternative to Delta-complexes and CW complexes. The proposed method is just an idea which we believe deserve further formal mathematical investigation.
Category: Topology
[84] viXra:1910.0547 [pdf] submitted on 2019-10-26 03:00:49
Authors: Volker Thürey
Comments: 8 Pages.
We present some thoughts about a coloring of an arbitrary map.
Category: Topology
[83] viXra:1910.0039 [pdf] submitted on 2019-10-05 06:42:28
Authors: Vincenzo Nardozza
Comments: 6 Pages.
In this paper we introduce the idea of a Solid Strip which is the generalization to higher dimensions of 2-dimensional untwisted Mobius strips.
Category: Topology
[82] viXra:1906.0367 [pdf] submitted on 2019-06-19 10:20:12
Authors: Riad Khidr Al-Hamido
Comments: 137 Pages.
يتعمق موضوع الأطروحة بد ا رسة الفضاءات متعددة التبولوجيا ومجموعاتيا المفتوحة والمغمقة, وفقاً لممفيوم
العادي ووفقاً لمنطق النتروسوفيك ذلك المنطق الجديد عالمياً والأعم من المنطق الضبابي, والذي أسسو
العالم الأمريكي F.Smarandache عام 1995 الذي يدرس وييتم بالحياد, بحيث ياخذ ىذا المنطق
الجديد بعين الاعتبار كل فكرة مع نقيضيا مع طيف الحياد , حيث ياخذ ىذا المنطق كل بيان بثلاث
ابعاد ىي الصح ) T ( بدرجات والخطأ ) F ( بدرجات والحياد ) I ( بدرجات, نعبر عن ذلك بالشكل ) T,I,F )
وىذ يعطي وصفاً اكثر دقة من المنطق الضبابي والمنطق الحدسي.
لقد قام العمماء بد ا رسة الفضاءات التبولوجية ومكوناتيا الأساسية من المجموعات المفتوحة والمغمقة, وبما
أن المجموعات المفتوحة والمغمقة تعد المبنة الرئيسية في بناء التبولوجيا والفضاء التبولوجي فقد توسع
العمماء والباحثون في د ا رستيا, حيث قدموا أنماطاً أضعف منيا مثل المجموعات المفتوحة )المغمقة( من
نمط الفا, والمجموعات المفتوحة )المغمقة( من نمط بيتا, المجموعات شبة المفتوحة )المغمقة(, ومن ثم
توسع الباحثون ومددوا مفيوم الفضاء التبولوجي الى الفضاء التبولوجي الثنائي عمى يد العالم كيمي عام
1965 في , - , ثم توسع الباحثون بد ا رستو وعمموا جميع تعاريف المجموعات المفتوحة )المغمقة( إلى
الفضاء التبولوجي الثنائي.
أما الفضاء التبولوجي الثلاثي فقد تم تعريفو ود ا رستو من قبل الباحث مارتن عام 2000 في , - .
عرف Mrsevic و I. L. Reilly عام 1996 في , - المجموعات المفتوحة من النمط S ,
والمجموعات المغمقة من النمط S ( ,S-closed sets (S-open sets في الفضاء التبولوجي الثنائي.
أيضاً عرف N. A. Jabbar و A. I. Nasir عام 2010 في , - المجموعات المفتوحة من النمط N
في الفضاء التبولوجي الثنائي.
عرف A. A. Salama and F. Smarandache , and V. Kroumov عام 2014 في , - مفيوم
الفضاء التوبولوجي النتروسوفيكي اليش كما عرفوا المجموعة النتروسوفيكية اليشة المفتوحة والمغمقة
والعمميات عمييا مثل التقاطع والاجتماع.
أيضاً قدم البروفيسور المصري احمد سلامة A.A. Salama عام 2013 د ا رسة حول مفيوم النقاط
النتروسوفيكية اليشة , - وعرف مفيوم انتماء عنصر ما لمجموعة نتروسوفيكية ىشة.
04
نتابع في ىذه الأطروحة د ا رسة الفضاءات التبولوجية ونركز د ا رستنا عمى الفضاءات متعددة التبولوجيا
منيا, وندرس ونعرف أنماطاً جديدة من المجموعات المفتوحة والمغمقة فييا, كما ندرس ونعرف الفضاءات
التبولوجيا النتروسوفيكية اليشة والفضاءات متعددة التبولوجيا النتروسوفيكية اليشة, ايضاً ندرس ونعرف
الفضاءات التبولوجيا النتروسوفيكية الثنائية وأنماطاً جديدة من المجموعات النتروسوفيكية فييا, لتعطي
إضافة ليا طابع ىام وجديد في ىذا المجال, حيث ركزنا عمى التعريف بمنطق النتروسوفيك الذي يفتح
المجال أمام الباحثين في كل الاختصاصات لا سيما الطبية وعموم الفيزياء والرياضيات عموماً والتبولوجيا
خصوصاً.
تعد أطروحتنا الد ا رسة الأولى من نوعيا التي تقوم بتطبيق المنطق النتروسوفيكي الجديد عمى التبولوجيا
والفضاءات التبولوجية في الجامعات السورية.
Category: Topology
[81] viXra:1905.0078 [pdf] submitted on 2019-05-04 07:01:16
Authors: Pierre-Yves Gaillard
Comments: 4 Pages.
To a topological space X we attach in two equivalent ways a profinite space X' and a continuous map F: X --> X' such that, for any continuous map f: X --> Y, where Y is a profinite space, there is a unique continuous map f': X' --> Y such that f'oF = f.
Category: Topology
[80] viXra:1902.0470 [pdf] submitted on 2019-02-27 15:22:11
Authors: Volker W. Thürey
Comments: 4 Pages.
We provide a charaterization of maps which are colourable with two colours
Category: Topology
[79] viXra:1811.0414 [pdf] submitted on 2018-11-27 00:29:55
Authors: Christopher Goddard
Comments: 22 Pages.
This short article follows an earlier document, wherein I indicated how the foundations of game theory could be reformulated within the lens of a more information theoretic and topological approach. Building on said work, herein I intend to generalise this to meta games, where one game (the meta-game) is built on top of a game, and then to meta-meta-games. Finally I indicate how one might take these ideas further, in terms of constructing frameworks to study policies, which relate to the solution of various algebraic invariants.
Category: Topology
[78] viXra:1810.0289 [pdf] submitted on 2018-10-19 01:18:11
Authors: Christopher Goddard
Comments: 10 Pages.
Within this paper, I combine ideas from information theory, topology and game theory, to develop a framework for the determination of optimal strategies within iterated cooperative games of incomplete information.
Category: Topology
[77] viXra:1810.0075 [pdf] submitted on 2018-10-05 13:26:05
Authors: Antoine Balan
Comments: 2 pages, written in english
We define here a cohomology called the X-cohomology with help of a closed 1-form X over the manifold.
Category: Topology
[76] viXra:1809.0308 [pdf] submitted on 2018-09-16 05:40:30
Authors: A.A. Salama, I.M.Hanafy, M. S. Dabash
Comments: 8 Pages.
The aim of this paper is devoted to introduce and study the concepts of semi-compact (resp.semi-Lindelӧf, locally semi-compact) spaces in a neutrosophic crisp topological space. Several properties, functions properties of neutrosophic crisp semi-compact spaces are studied. In addition to these, we introduce and study the definition of neutrosophic crisp semi-Lindelӧf spaces and neutrosophic crisp locally semi-compact spaces. We show that neutrosophic crisp semi-compact spaces is preserved under neutrosophic crisp irresolute function and neutrosophic crisp pre-semi-closed function with neutrosophic crisp semi-compact point inverses.
Category: Topology
[75] viXra:1809.0250 [pdf] submitted on 2018-09-13 04:50:44
Authors: Mirosław J. Kubiak
Comments: 4 Pages.
Some physicists believe that the spacetime, in absence of the matter, is empty. In this paper I presented an opposing point of view.
Category: Topology
[74] viXra:1807.0360 [pdf] submitted on 2018-07-21 19:51:00
Authors: Riad K Al-Hamido, Taleb gareba
Comments: 13 Pages.
This Paper is to introduce and define a new class of open set in
bitopological space called pre-Nα-open as generalized of pre-α-open in topological
space , and we study their basic properties
Category: Topology
[73] viXra:1807.0253 [pdf] submitted on 2018-07-13 08:04:57
Authors: Thinh D. Nguyen
Comments: 2 Pages.
We show that if one has ever loved reading Prasolov’s books, then one can move on reading our recent article [3] and several words following to deduce that partitioning a graph into triangles is not an easy problem.
Category: Topology
[72] viXra:1804.0234 [pdf] submitted on 2018-04-18 11:44:58
Authors: Onurcan Bektaş
Comments: 3 Pages.
For a given planar diagram of a closed & connected surface, we establish an algebraic method for cutting and gluing operations on the edges of the diagram. By this, by just manipulating the name of the edges with the given rules, we can determine the type of the surface without having need to draw any diagram.
Category: Topology
[71] viXra:1804.0170 [pdf] submitted on 2018-04-12 18:08:40
Authors: A. A. Salama, Hewayda ElGhawalby, Asmaa.M.Nasr
Comments: 14 Pages.
In this paper, we aim to develop a new type of neutrosophic crisp set called the retract neutrosophic crisp set and shows a grayscale image in a 2D Cartesian domain with neutrosophic crisp components in the neutrosophic domain. The introduced set is a retraction of any triple structured crisp set. Whereas, the retractset deduced from any neutrosophic crisp set is coincide its corresponding star neutrosophic crisp set defined in by Salama et al. [1]. Hence we construct a new type of neutrosophic crisp topological spaces, called the retract neutrosophic crisp topological space as a retraction of the star neutrosophic topological space. Moreover, we investigate some of its properties.
Category: Topology
[70] viXra:1711.0464 [pdf] submitted on 2017-11-28 21:22:54
Authors: Johan Noldus
Comments: 1 Page.
A simple proof of the generalized Poincare conjecture is presented.
Category: Topology
[69] viXra:1711.0463 [pdf] submitted on 2017-11-28 22:35:43
Authors: Johan Noldus
Comments: 1 Page.
A simple proof is given that for Morse cobordisms the Betti numbers are exactly equal to the number of critical Morsre points with corresponding index.
Category: Topology
[68] viXra:1711.0461 [pdf] submitted on 2017-11-28 23:31:47
Authors: Johan Noldus
Comments: 1 Page.
We formulate a considerable extension of the usual Morse theorem.
Category: Topology
[67] viXra:1711.0460 [pdf] submitted on 2017-11-29 01:53:30
Authors: Johan Noldus
Comments: 2 Pages.
We prove that the Betti numbers provide for a full topological classification.
Category: Topology
[66] viXra:1711.0445 [pdf] submitted on 2017-11-28 05:38:15
Authors: Johan Noldus
Comments: 2 Pages.
A new simple proof is given for the Brouwer fix point theorem.
Category: Topology
[65] viXra:1711.0301 [pdf] submitted on 2017-11-14 11:58:38
Authors: Edigles Guedes
Comments: 3 Pages.
In this paper, we construct an equation involving Alexander polynomials for knots 86 and 87.
Category: Topology
[64] viXra:1711.0253 [pdf] submitted on 2017-11-09 00:57:34
Authors: Nicholas R. Wright
Comments: 6 Pages.
We find that the Hodge conjecture is an overdetermined system rather than an underdetermined system, thereby becoming homogenous and leading to overfitting. A product of normal spaces need not be normal thereby initiating and reinforcing the conjecture. A norm should be found through regularization. We find the Magic Star polygon to be a satisfying norm. The Torelli theorem also gives deep and technical proof. Analysis can be seen through a multiple regression technique. Automorphism is not obtainable with a contradiction in the trivial and integral.
Category: Topology
[63] viXra:1710.0278 [pdf] submitted on 2017-10-24 06:22:09
Authors: Suehwan Jeong, Junho Yeo
Comments: 7 pages, Abstract available on English/Korean both, Main text Korean only
The Four Color Theorem(4CT) is the theorem stating that no more than four colors are required to color each part of a plane divided into finite parts so that no two adjacent parts have the same color. It was proven in 1976 by Kenneth Appel and Wolfgang Haken, but here we will prove 4CT without Computer Resources. We can display the picture to color as a graph, using nodes that are the points that represent each figure in the picture, and stects which is lines that links two nodes neighboring each other. We proved that every picture to be colored can be expressed as a liner graph, made up only with nodes and stects that have the shape of straight lines. We will name the triangle made of nodes and stects that contains other nodes and stect, ‘Triangular Convex Cell’. Also, we will call the graph that has the Triangular Convex Cell and also has the form of a convex set, a ‘Triangular Convex Cell graph’. The Euler characteristic in plane graph is 1, so if we regard the numver of the node v, the number of the stect e, and the number of the sides made by nodes and stects f, the equation v-e+f=1is established. Using this, we can derive the result that the graph with the highest total connection strength, which is the number of the connected graphs of each node in the graph, is a triangular-convex graph. Now, we prove the Triangular Convex Cell graph prove The Four Color Theorem regardless of how many nodes there are in the Triangular Convex Cell, or it’s arranged shape. We can use this to colorize a huge Triangular Convex Cell graph in which there are ∞ nodes inside the Triangular Convex Cell, and delete the nodes and the stects of the graph as needed to fit the picture to be colored. Thus, by using this method, it can be seen that the Four Color Theorem holds for all the pictures.
Category: Topology
[62] viXra:1710.0118 [pdf] submitted on 2017-10-10 23:07:27
Authors: Dmitri Martila
Comments: 4 Pages.
It is amazing to see, how the problems find their solutions. Even such extremely long as the 1200 pages of the ABC-hypothesis proof of the ``Japan Perelman'', which is needed to be consumed by the most brilliant men to come. And like the first PCs were huge but became compact, the large proofs can turn into very compact ones. \copyright
Category: Topology
[61] viXra:1709.0381 [pdf] submitted on 2017-09-25 05:22:17
Authors: Choe Ryujin
Comments: 5 Pages.
Solution of Inscribed Squares Problem
Category: Topology
[60] viXra:1707.0127 [pdf] submitted on 2017-07-09 11:29:59
Authors: Antoine Balan
Comments: 2 pages, written in french
A cohomology is defined with an automorphism of the tangent fiber bundle. The so defined cohomology is a topological invariant of the manifold considered.
Category: Topology
[59] viXra:1707.0065 [pdf] submitted on 2017-07-05 04:20:26
Authors: David Edwards, Robert Varley
Comments: 7 Pages.
We define Adelic Homotopy Theory and compare it with Rational Homotopy Theory.
Category: Topology
[58] viXra:1706.0547 [pdf] submitted on 2017-06-28 13:16:36
Authors: Arturo Tozzi, James F Peters, Raquel del Moral, Pedro C Marijuan
Comments: 10 Pages.
A unifying principle underlies the organization of physical and biological systems. It relates to a well-known topological theorem which succinctly states that an activity on a planar circumference projects to two activities with “matching description” into a sphere. Here we ask: What does “matching description” mean? Has it something to do with “identity”? Going through different formulations of the principle of identity, we describe diverse possible meanings of the term “matching description”. We demonstrate that the concepts of “sameness”, “equality”, “belonging together” stand for intertwined levels with mutual interactions. By showing that “matching” description is a very general and malleable concept, we provide a novel testable approach to “identity” that yields helpful insights into physical and biological matters. Indeed, we illustrate how a novel mathematical approach derived from the Borsuk-Ulam theorem, termed bio-BUT, might explain the astonishing biological “multiplicity from identity” of evolving living beings as well as the logic of their intricate biochemical arrangements.
Category: Topology
[57] viXra:1703.0035 [pdf] submitted on 2017-03-04 09:18:56
Authors: Antoine Balan
Comments: 1 Page. written in French
We define here an homology for a manifold called edge homology.
Category: Topology
[56] viXra:1701.0649 [pdf] submitted on 2017-01-28 01:09:57
Authors: Arturo Tozzi
Comments: 3 Pages.
Recently introduced versions of the Borsuk-Ulam theorem (BUT) state that a feature on a n-manifold projects to two features with matching description onto a n+1 manifold. Starting from this rather simple “abstract” claim, a fruitful general framework has been built, able to elucidate disparate “real” physical and biological phenomena, from quantum entanglement, to brain activity, from gauge theories to pre- big bang scenarios. One of the main concerns of such a topological approach to systems features is that it talks in rather general terms, leaving apart the peculiar features of individuals and of single physical and biological processes. In order to tackle this issue, in this brief note we ask: what does it mean “matching description”? has matching description anything to do with “identity”?
Category: Topology
[55] viXra:1701.0519 [pdf] submitted on 2017-01-17 00:26:31
Authors: W. B. Vasantha Kandasamy, K. Ilanthenral, Florentin Smarandache
Comments: 278 Pages.
In this book authors for the first time develop the notion of MOD natural neutrosophic subset special type of topological spaces using MOD natural neutrosophic dual numbers or MOD natural neutrosophic finite complex number or MOD natural neutrosophic-neutrosophic numbers and so on to build their respective MOD semigroups. Later they extend this concept to MOD interval subset semigroups and MOD interval neutrosophic subset semigroups. Using these MOD interval semigroups and MOD interval natural neutrosophic subset semigroups special type of subset topological spaces are built. Further using these MOD subsets we build MOD interval subset matrix semigroups and MOD interval subset matrix special type of matrix topological spaces. Likewise using MOD interval natural neutrosophic subsets matrices semigroups we can build MOD interval natural neutrosophic matrix subset special type of topological spaces. We also do build MOD subset coefficient polynomial special type of topological spaces. The final chapter mainly proposes several open conjectures about the validity of the Kakutani’s fixed point theorem for all MOD special type of subset topological spaces.
Category: Topology
[54] viXra:1612.0338 [pdf] submitted on 2016-12-24 17:35:46
Authors: Pablo Álvarez Domínguez
Comments: 3 Pages.
The main objectives of this little work is to propose a conjecture about a condition that
every Kissing Number must satisfy and to study a little bit its most basic direct
consequences if it were proven true. It can seem that nowadays there is not enough
acknowledge to conjecture it (mainly because the little information we have about Kissing
Numbers). However, the few known examples we have about this type of numbers satisfy
it.
Category: Topology
[53] viXra:1611.0322 [pdf] submitted on 2016-11-24 03:27:16
Authors: A.a.salama, I.m.hanafy, Hewayda Elghawalby, M.s.dabash
Comments: 10 Pages.
In this paper, we introduce and study the concept of "neutrosophic crisp closed set "and
"neutrosophic crisp continuous function. Possible application to GIS topology rules are touched
upon.
Category: Topology
[52] viXra:1610.0223 [pdf] submitted on 2016-10-19 03:29:22
Authors: Arturo Tozzi, James F Peters
Comments: 8 Pages.
The (spatial) fractals and (temporal) power laws are ubiquitously displayed by large classes of biological systems. Nevertheless, they are controversial phenomena with still unexplained genesis. From the far-flung branch of topology, a helpful concept comes into play, namely the Borsuk-Ulam theorem, shedding new light on the scale-free origin’s long-standing enigma. The theorem states that a single point, if embedded in just one spatial dimension higher, gives rise to two antipodal points that have matching descriptions and similar features. Here we demonstrate that, when we introduce into a system the proper fractal extra-dimension instead of a spatial one, we are able to achieve two antipodal self-similar shapes, corresponding to the distinctive scale-free’s higher and lower magnifications. By showing that the elusive phenomena of fractals and power laws can be explained and analyzed in a topological framework, we make clear why the Borsuk-Ulam theorem is the most general principle underlying their pervasive occurrence in nature.
Category: Topology
[51] viXra:1610.0222 [pdf] submitted on 2016-10-19 03:34:00
Authors: Arturo Tozzi, James F Peters
Comments: 8 Pages.
Nonlinear chaotic dynamics are widespread, both in physical and biological systems. This form of dynamics is frequently studied through logistic maps equipped with bifurcations, where intervals are dictated by the Feigenbaum constants. In such a multifaceted framework, a concept from the far-flung branch of topology, namely the Borsuk-Ulam theorem, comes into play. The theorem tells us that a continuous mapping from antipodal points with matching feature values on an n-sphere to the same real value can always be found. Here we demonstrate that embracing nonlinearity in the framework of the Borsuk-Ulam theorem means that bifurcation transformations (the antipodal points) can be described as paths or trajectories on abstract spheres equipped with a Feigenbaum dimension. Such an approach allows the evaluation of nonlinear systems through linear techniques. In conclusion, we provide a general topological mechanism which explains the elusive chaotic phenomena, cast in a physical/biological fashion which has the potential of being operationalized.
Category: Topology
[50] viXra:1609.0084 [pdf] submitted on 2016-09-07 07:48:06
Authors: Mirosław J. Kubiak
Comments: 7 Pages.
We proposed a description of the gravitational phenomena in a new medium, which merges the Minkowski four-dimensional spacetime and the bare mass density into the single idea. Under influence outer gravitational field the Minkowski four-dimensional spacetime does not change, while the bare mass density changing and becomes the effective mass density. This is an alternative attempt to describe gravitational phenomena, using a new idea of massification of the spacetime.
Category: Topology
[49] viXra:1608.0003 [pdf] submitted on 2016-08-01 11:41:37
Authors: Richard L Amoroso
Comments: 39 Pages.
We thank Newton for inspiring strict adherence to hypotheses non-fingo1,and claim reasonable a posteriori surety in positing the need for an
Ontological-Phase Topological Field Theory (OPTFT) as the final step in
describing the remaining requirements for bulk UQC. Let’s surmise with
little doubt that a radical new theory needs to be correlated with the
looming 3rd regime of Unified Field Mechanics (UFM). If the author
knows one thing for sure, it is that gravity is not quantized! The physics
community is so invested in quantizing the gravitational force that it could
still be years away from this inevitable conclusion. There is still a serious
conundrum to be dealt with however; discovery of the complex Manifold
of Uncertainty (MOU), the associated ‘semi-quantum limit’ and the fact
of a duality between Newton’s and Einstein’s gravity, may allow some
sort of wave-particle-like duality with a quantal-like virtual graviton in the
semi-quantum limit. Why mention the gravitational field? Relativistic
information processing (RIP) introduces gravitational effects in the
‘parallel transport’ aspects of topological switching in branes. There are A
and B type topological string theories, and a related Topological MTheory
with mirror symmetry, that are somewhat interesting especially
since they allow sufficient dimensionality with Calabi-Yau mirror
symmetry perceived as essential elements for developing a UFM. But a
distinction between these theories and the ontology of an energyless
topological switching of information (Shannon related) through
topological charge in brane dynamics, perhaps defined in a manner
making correspondence to a higher dimensional (HD) de-Broglie-Bohm
super-quantum potential synonymous with a 'Force of coherence' of the
unified field is of interest. Thus the term 'OPTFT’ has been chosen to address this issue as best as the Zeitgeist is able to conceive at the time of writing…
Category: Topology
[48] viXra:1605.0237 [pdf] submitted on 2016-05-22 14:15:00
Authors: Luis Sancho
Comments: 355 Pages.
The 5th dimension is in the discontinuities of the real line, which grow as we look into smaller scales, till becoming infinite.
The 5th dimension creates different geometries for each different world.
From the human relative frame of reference, the observer has an Euclidean view of its scale, a hyperbolic view of smaller quantum systems and an elliptic view of larger gravitational worlds, according to the ratio between its informative curvature, Tƒ and length of its space quanta Sp.
The symmetries that web bidimensional planes of space with tall, cyclical frequencies of time create the 4D Space-time beings of the fractal Universe, constantly moving, generating, growing, reproducing, evolving new fractal scales of the 5th dimension.
But as time passes the densities of its frequency of time cycles, Tƒ, grow and the system curves in excess, ageing and finally completing a 0-sum closed curve,, ending a world cycle in which the topological transformations of the being, are seen as its 3 ages each one a phase of its r=evolution as a world-view.
Category: Topology
[47] viXra:1601.0106 [pdf] submitted on 2016-01-10 13:54:58
Authors: Alex Patterson
Comments: 4 Pages. Paper 1, of program.
Using Functor Substitutability for the basis of creating an intuitionist interpretation of the results of that subscribe. Laying the Grounds for Challenging Goedel's Incompleteness Theorems with the Aspects of the Poincare Group. Proceeding with: Propositional Quantum Logic, Transitioning “Non-Commensurable” Smoothly to Functor-Auxiliary Substitutability and Detachment.
Category: Topology
[46] viXra:1601.0031 [pdf] submitted on 2016-01-05 10:40:24
Authors: H.E. Winkelnkemper
Comments: 7 Pages.
Using Artin Presentation Theory, we mathematically augment a
remark of Atiyah on physics and Donaldson's 4D theory which, conversely, explicitly
introduces the theoretical physical relevance of AP Theory into Modern
Physics. AP Theory is a purely discrete group-theoretic, in fact, a framed pure
braid theory, which, in the sharpest possible holographic manner, encodes all
closed, orientable 3-manifolds and their knot and linking theories, and a large
class of compact, connected, simply-connected, smooth 4-manifolds with a connected
boundary, whose physical relevance for Atiyah's remark we explain.
Category: Topology
[45] viXra:1512.0456 [pdf] submitted on 2015-12-28 04:12:15
Authors: Alex Patterson
Comments: 19 Pages. Ability to go and move on Against Method, pace PKF spoon listserve archive
A demonstration of using Against Method, of Paul K. Feyerabend.
Category: Topology
[44] viXra:1510.0057 [pdf] submitted on 2015-10-06 03:47:10
Authors: Dmitri Martila
Comments: 4 Pages.
There is Prize committee (claymath.org), which requires publication in worldwide reputable mathematics journal and at least two years of following scientific admiration. Why then the God-less Grisha Perelman has published only in a
God-less forum (arXiv), publication was unclear as the crazy sketch; but mummy child "Grisha" has being forced to accept the Millennium Prize? Am I simply ugly or poor? Please respect my copyrights!
Category: Topology
[43] viXra:1507.0204 [pdf] submitted on 2015-07-27 18:50:52
Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 225 Pages.
In this book for the first time the authors introduce a special type of topological spaces using the interval [0, n). Several of the properties enjoyed by these special spaces are analyzed. Over hundred problems are suggested, some of which are open conjectures. This book gives a new perspective to topological spaces.
Category: Topology
[42] viXra:1506.0184 [pdf] submitted on 2015-06-25 19:16:39
Authors: a. a. Salama
Comments: 5 Pages.
Since the world is full of indeterminacy, the neutrosophics
found their place into contemporary research. The fundamental
concepts of neutrosophic set, introduced by Smarandache
in [30, 31, 32] and Salama et al. in [4-29]. In Geographical
information systems (GIS) there is a need to model spatial regions with indeterminate boundary and under indeterminacy. In this paper the structure of some classes of neutrosophic crisp nearly open sets are investigated and some applications are given.Finally we generalize the crisp topological and intuitioistic studies to the notion of neutrosophic crisp set. Possible applications
to GIS topological rules are touched upon.
Category: Topology
[41] viXra:1506.0139 [pdf] submitted on 2015-06-18 12:06:37
Authors: Luis Sancho
Comments: 55 Pages.
We expand the holographic principle to explain the nature of the universe and all its fractal 2-manifold organisms.
The simplest explanation of the complex universe departs from the holographic principle: information, form is bidimensional. Because all what we perceive is the 'cover' of things, its membranes.
Thus in a 2-manifold, in a bidimensional world there are only 2 topologies, which correspond to the main parts of any system, the lineal, energetic and spherical informative dimensions or motions (since energy is just space in motion and time information cyclical form in motion). And its 'wavelike combinations, exi.
And we shall call energy, to th expansive motions, which form limbs, often with hyperbolic topology (bilateral).
And we shall call information to the implosive vortices, which form particles and heads, often of spherical geometry.
And the space between them the 3 membrane-topology of the universe, its body wave, the ExI part of the system.
Thus all what exists are polar systems, with 'energy fields/limbs' and informative heads/particles, exchange energy and information creating a 3rd element, 'waves-bodies'.
Category: Topology
[40] viXra:1410.0132 [pdf] submitted on 2014-10-22 17:33:09
Authors: A. A. Salama, Said Broumi, Florentin Smarandache
Comments: 8 Pages.
The focus of this paper is to propose a new
notion of neutrosophic crisp sets via neutrosophic crisp
ideals and to study some basic operations and results in
neutrosophic crisp topological spaces. Also,
neutrosophic crisp L-openness and neutrosophic crisp Lcontinuity
are considered as a generalizations for a crisp
and fuzzy concepts. Relationships between the above
new neutrosophic crisp notions and the other relevant
classes are investigated. Finally, we define and study
two different types of neutrosophic crisp functions.
Index Terms—Neutrosophic Crisp Set; Neutrosophic
Crisp Ideals; Neutrosophic Crisp L-open Sets;
Neutrosophic Crisp L- Continuity; Neutrosophic Sets.
I. INTRODUCTION
The fuzzy set was introduced by Zadeh [20] in 1965,
where each element had a degree of membership. In
1983 the intuitionstic fuzzy set was introduced by K.
Atanassov [1, 2, 3] as a generalization of fuzzy set,
where besides the degree of membership and the degree
of non- membership of each element. Salama et al [11]
defined intuitionistic fuzzy ideal and neutrosophic ideal
for a set and generalized the concept of fuzzy ideal
concepts, first initiated by Sarker [19]. Smarandache [16,
17, 18] defined the notion of neutrosophic sets, which is
a generalization of Zadeh's fuzzy set and Atanassov's
intuitionistic fuzzy set. Neutrosophic sets have been
investigated by Salama et al. [4, 5, 6, 7, 8, 9, 10, 11, 12,
13, 14, 15]. In this paper is to introduce and study some
new neutrosophic crisp notions via neutrosophic crisp
ideals. Also, neutrosophic crisp L-openness and
neutrosophic crisp L- continuity are considered.
Relationships between the above new neutrosophic crisp
notions and the other relevant classes are investigated.
Recently, we define and study two different types of
neutrosophic crisp functions.
The paper unfolds as follows. The next section briefly
introduces some definitions related to neutrosophic set
theory and some terminologies of neutrosophic crisp set
and neutrosophic crisp ideal. Section 3 presents
neutrosophic crisp L- open and neutrosophic crisp Lclosed
sets. Section 4 presents neutrosophic crisp L–
continuous functions. Conclusions appear in the last section.
Category: Topology
[39] viXra:1409.0124 [pdf] submitted on 2014-09-16 03:54:14
Authors: Vincenzo Nardozza
Comments: 10 Pages.
By means of a computer, all the possible homogeneous compact 3-Delta-complexes made up of a small number of simplexes (from 1 to 3) have been classified in homology classes. The analysis shows that, with a small number of simplexes, it is already possible to build quite a large number of separate topological spaces.
Category: Topology
[64] viXra:2401.0094 [pdf] replaced on 2024-02-17 23:07:54
Authors: Alfonso De Miguel bueno
Comments: 23 Pages. 23 figures (Note by viXra Admin: Please use the viXra Number 2401.0094 when making replacement)
This preprint introduces in a visual and conceptual way a model of two intersecting curved fields with a shared nucleus, whose quantized dynamics offer potential cases of the four-variable Jacobian conjecture and a nonlinear Hodge cycle. The Kummer type geometry of the model suggests a unified framework where abstract mathematical developments like Tomita-Takesaki, Gorenstein, and Dolbeault theories, can be conceptually linked to the Jacobian, Hodge, and Riemann conjectures. Other mathematical physics topics, like the mass gap problem, releflection positivity, the arise of an imaginary time, or t-duality are also described within this context. The model also lays the foundation of a novel deterministic quantum atomic system with a supersymmetric dual nucleus structure of matter and mirror antimatter.
Category: Topology
[63] viXra:2401.0094 [pdf] replaced on 2024-01-24 22:23:47
Authors: Alfonso De Miguel bueno
Comments: 13 Pages. 18 figures
This paper introduces a topological model based on two intersecting fields varying either same or opposite phase that may graphically illustrate the Jacobian conjecture for four variables. It also suggests connections with other mathematical topics as Gorenstein Liaison, Tomita-Takesaki modular theory, the Mass gap problem, Reflection positivity, or T-duality in string theory, all considered within the same framework. Being applicable to the Jacobian conjecture, the model would represent a confirmation case in both the symmetric and antisymmetric systems. However, in the symmetric system the mirror reflection property would not be considered by the conjecture when it comes to the vertical subfields.The model has been developed in the context of the physics beyond the Standard theory as an unconventional atomic system whose nucleus is formed by mirror matter and antimatter. It is generally described in the last section.
Category: Topology
[62] viXra:2307.0035 [pdf] replaced on 2023-09-03 01:04:46
Authors: Yung Zhao
Comments: 3 Pages.
It is deduced from Bertrand's Postulate that every even integer greater than 4 is the sum of two primes.
Category: Topology
[61] viXra:2208.0074 [pdf] replaced on 2023-09-05 23:48:49
Authors: Savinov Sergei
Comments: 2 Pages.
The preprint provides a consideration of limiting the lower limit of the chromatic number to 7.
Category: Topology
[60] viXra:2207.0115 [pdf] replaced on 2022-10-22 19:25:22
Authors: Thomas Halley
Comments: 13 Pages.
Let k( i^ ) not equal to m. We define an arrow. We show that D = 0. Thompson’s computation of ideals was a milestone in parabolic knot theory. In contrast to [2], a useful suggestion of the subject can be found following Conjecture 6.2 concluding this paper. Does the Goldbach Conjecture form a knot with no openings on the given sensitive even numbers? They do partially and differentially on the extrema and local bound of -2. The circle must be cut at radius 2 when a+b=2r. The resultant has been formally found in [1] and is further described in this paper.
Category: Topology
[59] viXra:2001.0352 [pdf] replaced on 2020-05-18 17:16:55
Authors: Vincenzo Nardozza
Comments: 11 Pages.
We discuss a new method for representing Compact Manifolds.
Category: Topology
[58] viXra:2001.0352 [pdf] replaced on 2020-03-21 17:33:17
Authors: Vincenzo Nardozza
Comments: 11 Pages.
In this paper we discuss a new method for representing Compact Manifolds.
Category: Topology
[57] viXra:2001.0161 [pdf] replaced on 2022-01-23 13:36:59
Authors: Theophilus Agama
Comments: 8 Pages. A few technicalities resolved regarding the scale of compression and the inequality in the notion of points contained in a compression ball has been made strict. This is because the case of equality is treated separately as admissible points.
In this paper we apply the method of compression to construct a dense set of points in the plane at rational distance from each other. We provide a positive solution to the Erd˝os-Ulam problem.
Category: Topology
[56] viXra:2001.0161 [pdf] replaced on 2021-09-04 21:13:50
Authors: Theophilus Agama
Comments: 11 Pages. A revision file with detailed proof of the Erdos-Ulam conjecture
In this paper we introduce and develop the topology of compression of points in space. We use this Topology to solve the Erd\H{o}s-Ulam problem. We provide a positive solution in this paper.
Category: Topology
[55] viXra:1912.0161 [pdf] replaced on 2020-02-08 17:31:41
Authors: Vincenzo Nardozza
Comments: 10 Pages.
We introduce the idea of Solid Strip Configurations which is a way of construction 3-dimensional compact manifolds alternative to $\Delta$-complexes and CW complexes. The proposed method is just an idea which we believe deserve further formal mathematical investigation.
Category: Topology
[54] viXra:1912.0161 [pdf] replaced on 2020-01-11 16:20:10
Authors: Vincenzo Nardozza
Comments: 11 Pages.
We introduce the idea of Solid Strip Configurations which is a way of describing 3-dimensional compact manifolds alternative to $\Delta$-complexes and CW complexes. The proposed method is just an idea which we believe deserve further formal mathematical investigation.
Category: Topology
[53] viXra:1910.0039 [pdf] replaced on 2019-11-29 14:46:58
Authors: Vincenzo Nardozza
Comments: 11 Pages.
In this paper we introduce the idea of a Solid Strip which is the generalization to higher dimensions of 2-dimensional Untwisted and Mobius Strips.
Category: Topology
[52] viXra:1910.0039 [pdf] replaced on 2019-11-03 11:28:53
Authors: Vincenzo Nardozza
Comments: 8 Pages.
In this paper we introduce the idea of a Solid Strip which is the generalization to higher dimensions of 2-dimensional Untwisted and Mobius Strips.
Category: Topology
[51] viXra:1810.0075 [pdf] replaced on 2018-10-07 08:36:59
Authors: Antoine Balan
Comments: 2 pages, written in english
We define here a cohomology called the X-cohomology with help of a closed 1-form X over the manifold.
Category: Topology
[50] viXra:1804.0234 [pdf] replaced on 2018-04-19 22:40:24
Authors: Onurcan Bektaş
Comments: 3 Pages.
For a given planar diagram of a closed & connected surface, we establish an ”algebraic” method for cutting and gluing operations on the edges of the diagram. By this, by just manipulating the name of the edges with the given rules, with the guidance of the classification of closed and connected surface theorem given in [1], we can determine the type of the surface without having need to draw any diagram.
Category: Topology
[49] viXra:1804.0234 [pdf] replaced on 2018-04-18 22:28:34
Authors: Onurcan Bektaş
Comments: 3 Pages.
For a given planar diagram of a closed & connected surface, we establish an algebraic method for cutting and gluing operations on the edges of the diagram. By this, by just manipulating the name of the edges with the given rules, we can determine the type of the surface without having need to draw any diagram.
Category: Topology
[48] viXra:1711.0460 [pdf] replaced on 2017-12-15 16:00:34
Authors: Johan Noldus
Comments: 2 Pages.
We prove that the Betti numbers provide for a full topological classification.
Category: Topology
[47] viXra:1711.0445 [pdf] replaced on 2017-11-28 11:34:58
Authors: Johan Noldus
Comments: 2 Pages.
A new simple proof is given for the Brouwer fix point theorem.
Category: Topology
[46] viXra:1711.0253 [pdf] replaced on 2022-01-27 07:04:26
Authors: Nicholas R. Wright
Comments: 6 Pages. Demonstrating the Stein manifold in 8 dimensions.
We find that the Hodge conjecture is an overdetermined system rather than an underdetermined system, thereby becoming homogenous and leading to overfitting. A product of normal spaces need not be normal thereby initiating and reinforcing the conjecture. A norm should be found through regularization. We find the Magic Star polygon to be a satisfying norm. The Torelli theorem also gives deep and technical proof. Analysis can be seen through a multiple regression technique. Automorphism is not obtainable with a contradiction in the trivial and integral.
Category: Topology
[45] viXra:1711.0253 [pdf] replaced on 2019-08-14 14:20:37
Authors: Nicholas R. Wright
Comments: 6 Pages. Demonstrating the Stein manifold in 8 dimensions.
We find that the Hodge conjecture is an overdetermined system rather than an underdetermined system, thereby becoming homogenous and leading to overfitting. A product of normal spaces need not be normal thereby initiating and reinforcing the conjecture. A norm should be found through regularization. We find the Magic Star polygon to be a satisfying norm. The Torelli theorem also gives deep and technical proof. Analysis can be seen through a multiple regression technique. Automorphism is not obtainable with a contradiction in the trivial and integral.
Category: Topology
[44] viXra:1710.0278 [pdf] replaced on 2017-12-18 03:31:34
Authors: Suehwan Jeong, Junho Yeo
Comments: 9 Pages.
The Four Color Theorem (4CT) is the theorem stating that no more than four colors are required to color each part of a plane divided into finite parts so that no two adjacent parts have the same color. It was proven in 1976 by Kenneth Appel and Wolfgang Haken, but in this paper, we will prove 4CT simply without computer resources.
Category: Topology
[43] viXra:1705.0210 [pdf] replaced on 2017-05-20 07:34:40
Authors: Saenko V.I.
Comments: 3 Pages. This is the Russian version, the English one is directed to the peer-reviewed journal
It is proved that the irreducible map according to Franklin consists of 5 regions and, as a consequence, 4 colors are sufficient for colouring any map on the sphere
Category: Topology
[42] viXra:1609.0084 [pdf] replaced on 2017-03-06 13:46:39
Authors: Mirosław J. Kubiak
Comments: 7 Pages.
Until the early twentieth century, the three-dimensional space and one-dimensional time were considered separate beings. In 1909, German mathematician H. Minkowski connected together space and time into single idea, creating a new the four-dimensional spacetime.
In this paper we proposed the extension of this idea by the connection together the Minkowski four-dimensional spacetime and the mass density into the single idea, creating a new entity: the four-dimensional spacetime with the mass density.
Category: Topology
[41] viXra:1608.0003 [pdf] replaced on 2016-08-02 04:07:46
Authors: Richard L
Comments: 26 Pages. Forgot authors name, also reformatted
We thank Newton for inspiring strict adherence to hypotheses non-fingo, and claim reasonable a posteriori surety in positing the need for an Ontological-Phase Topological Field Theory (OPTFT) as the final step in describing the remaining requirements for bulk UQC. Let’s surmise with little doubt that a radical new theory needs to be correlated with the looming 3rd regime of Unified Field Mechanics (UFM). If the author knows one thing for sure, it is that gravity is not quantized! The physics community is so invested in quantizing the gravitational force that it could still be years away from this inevitable conclusion. There is still a serious conundrum to be dealt with however; discovery of the complex Manifold of Uncertainty (MOU), the associated ‘semi-quantum limit’ and the fact of a duality between Newton’s and Einstein’s gravity, may allow some sort of wave-particle-like duality with a quantal-like virtual graviton in the semi-quantum limit. Why mention the gravitational field? Relativistic information processing (RIP) introduces gravitational effects in the ‘parallel transport’ aspects of topological switching in branes. There are A and B type topological string theories, and a related Topological M-Theory with mirror symmetry, that are somewhat interesting especially since they allow sufficient dimensionality with Calabi-Yau mirror symmetric dual 3-tori perceived as essential elements for developing a UFM. But a distinction between these theories and the ontology of an energyless topological switching of information (Shannon related) through topological charge in brane dynamics, perhaps defined in a manner making correspondence to a higher dimensional (HD) de-Broglie-Bohm super-quantum potential synonymous with a 'Force of coherence' of the unified field is of interest. Thus the term 'OPTFT’ has been chosen to address this issue as best as the Zeitgeist is able to conceive at the time of writing…
Category: Topology
[40] viXra:1605.0237 [pdf] replaced on 2019-08-11 13:50:26
Authors: Luis sancho
Comments: 687 Pages.
We divide the study of Non-Euclidean, Non-Aristotelian 5D Mathematics in 3 parts, Space Geometry, Scalar Algebra & a brief introduction to the foundations of Time calculus.
Logic and math are the 2 entangled stiences of spacetime laws. As such in a Universe made of space-time beings, contrary to belief they are the most experimental of all stiences. Mathematics is the main science of vital, scalar Space (represented by spatial points and scalar numbers), in mirror symmetry with the less developed Time focused science of ¡ logic that analyzes the 5 Time dimotions of reality, as humans use only 1 time arrow -entropy- but 'God the seer of time is of a logic higher than man's' Augustine.
We dedicate 2 papers to maths main 2 subfields, S@-Geometry & ∆T-Algebra.
In this one we upgrade Nº theory & geometry to show mathematics as a logic mirror of the Universe's pentalogic scalar structure made with scalar numbers, Non-E fractal points with inner dimensions and timespace S<≈>T operands that reflect the dynamic symmetries & stœps of its 5 spacetime dimotions. Ænthropic men instead justify math with an ego-trip of digital creationism: Only he & God speak the language, math, that creates reality -not the other way around, and try to prove its truths with an incomplete (Gödel) axiomatic method, as an ideal, perfect absolute 'truth' with NO correspondence with reality (sets as 'imagined' units of math). We shall do the opposite: departing from reality we construct a vital improved mirror of maths, where even the perceived irregularities of mathematics are experimental true symmetries of a vital dynamic Universe: i.e. irrational numbers are required NOT to close a vital pi-cycle and √2 triangle to allow openings into its lower decimal scales to absorb energy and information. So we shouldn't force 'idealist continuity' in a discontinuous Universe. i.e. 3 topologic geometries with motion suffice to mirror the 3 St, sT, ST combinations of an organism because we ARE spacetime'. i.e. numbers are indistinguishable social groups (polytopes) because 5D is 'social'; its Prime, T>S + odd, S
Category: Topology
[39] viXra:1506.0139 [pdf] replaced on 2015-07-11 05:48:01
Authors: Luis Sancho
Comments: 32 Pages.
We expand the holographic principle to explain the nature of the universe and all its fractal 2-manifold organisms. The simplest explanation of the complex universe departs from the holographic principle: information, form is bidimensional. Because all what we perceive is the 'cover' of things, its membranes. Thus in a 2-manifold, in a bidimensional world there are only 2 topologies, which correspond to the main parts of any system, the lineal, energetic and spherical informative dimensions or motions (since energy is just space in motion and time information cyclical form in motion). And its 'wavelike combinations, exi. And we shall call energy, to th expansive motions, which form limbs, often with hyperbolic topology (bilateral). And we shall call information to the implosive vortices, which form particles and heads, often of spherical geometry. And the space between them the 3 membrane-topology of the universe, its body wave, the ExI part of the system. Thus all what exists are polar systems, with 'energy fields/limbs' and informative heads/particles, exchange energy and information creating a 3rd element, 'waves-bodies'.
We use the formalism to unify all disciplines of human knowledge, showing all its species display 5 isomorphisms, derived of the 3 topologic varieties:
- isomorphism of 3 finite, diffeomorphic dimensions of space
- isomorphism of 3 time-ages/states, past- young energy, liquid balanced present and solid, future, wrinkled age
- isomorphism of 3 space-time topologies, energy, iteration and information
- isomorphism of 3 hierarchies of organisation, the quantum/cellular, i-ndividual/human and social/cosmic scale
- isomorphism of 3 actions, energy feeding, reproductive iteration and informative gauging.
Whereas the 4 dimensional universe is the holographic intersection of 2-manifold membranes, and the Whole Universe a fractal sum of all of them
Category: Topology
[38] viXra:1409.0124 [pdf] replaced on 2015-08-17 09:28:44
Authors: Vincenzo Nardozza
Comments: 4 Pages.
By means of a computer, all the possible homogeneous compact generalised triangulations made up of a small number of 3-simplexes (from 1 to 3) have been classified in homology classes. The analysis shows that, with a small number of simplexes, it is already possible to build quite a large number of separate topological spaces.
Category: Topology
[37] viXra:1409.0124 [pdf] replaced on 2014-09-26 05:16:45
Authors: Vincenzo Nardozza
Comments: 10 Pages.
By means of a computer, all the possible homogeneous compact Generalised Triangulations made up of a small number of 3-simplexes (from 1 to 3) have been classified in homology classes. The analysis shows that, with a small number of simplexes, it is already possible to build quite a large number of separate topological spaces.
Category: Topology
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