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[71] 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
[70] 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
[69] 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
[68] 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
[67] 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
[66] 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
[65] 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
[64] 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
[63] 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
[62] 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
[61] 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
[60] 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
[59] 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
[58] 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
[57] 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
[56] 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
[55] 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
[54] 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
[53] 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
[52] 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
[51] 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
[50] 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
[49] 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
[48] 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
[47] 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
[46] 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
[45] 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
[44] 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
[43] 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
[42] 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
[41] 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
[40] 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
[39] 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
[38] 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
[37] 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
[36] 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
[35] 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
[34] 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
[33] 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
[32] 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
[31] 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$-quotient functions and study some of their
properties.
Category: Topology
[30] viXra:2001.0393 [pdf] submitted on 2020-01-20 06:45:34
Authors: Saeid Jafari, M. Parimala
Comments: 14 Pages.
The purpose of this paper is to introduce a new type of open sets called mI-open
sets and quasi-$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
[29] 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
[28] 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\~$$\alpha$-open sets and study some of its applications.
Category: Topology
[27] viXra:2001.0390 [pdf] submitted on 2020-01-20 06:59:47
Authors: A. Selvakumar, Saeid Jafari
Comments: 19 Pages.
In this paper, we introduce the notion of $I_{g~\alpha}$ -closed sets in ideal topological spaces and
investigate some of their properties. Further, we introduce the concept of mildly $I_{g~\alpha}$-
closed sets and $I_{g~\alpha}$-normal space.
Category: Topology
[26] viXra:2001.0388 [pdf] submitted on 2020-01-20 07:03:27
Authors: A. Selvakumar, Saeid Jafari
Comments: 10 Pages.
The basic objective of this paper is to introduce and investigate the properties of Nano $g\~$$\alpha$-closed sets in Nano topological spaces.
Category: Topology
[25] 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
[24] 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
[23] 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
[22] 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
[21] 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
[20] 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
[19] 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
[18] 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
[17] 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
[16] 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
[15] 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
[14] 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
[13] 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
[12] 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
[11] 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
[10] 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
[9] 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
[8] 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
[7] 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
[6] 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
[5] 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
[4] 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
[3] 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
[2] 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
[1] 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
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