Topology

2001 Submissions

[41] viXra:2001.0412 [pdf] submitted on 2020-01-20 16:40:58

On Certain Types of Notions Via Preopen Sets

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

Bioperations on $\alpha$-Separations Axioms in Topological Spaces

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

G*bp-Continuous, Almost G*bp-Continuous and Weakly G*bp-Continuous Functions

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

A Note on Properties of Hypermetric Spaces

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

On Generalized Closed Sets and Generalized Pre-Closed Sets in Neutrosophic Topological Spaces

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

Soft Interval Valued Intuitionistic Fuzzy Semi-Pre Generalized Closed Sets

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

Intuitionistic Fuzzy Ideals on Approximation Systems

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

Operation Approach of $g\star$-Closed Sets in Ideal Topological Spaces

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

Regularity and Normality Via $\beta \theta$-Open Sets

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

On the Class of Semipre-$\theta$-Open Sets in Topological Spaces

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

New Types of Continuous Functions Via $G \~$ \alpha$-Open Sets

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

$mi$-Open Sets and Quasi-$mi$-Open Sets in Terms of Minimal Ideal Topological Spaces

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

Some Properties of $g\~$$\alpha$-Closed Graphs

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

Contra $g\~$$\alpha$-Continuous Functions

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

On New Type of Sets in Ideal Topological Spaces

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

Nano $g\~$$\alpha$-Closed Sets in Nano Topological Spaces

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

$g\~$$\alpha$-Closed Sets in Terms of Grills

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

$g\~$$\alpha$-Closed Sets in Topological Spaces

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

Weak Separation Axioms Via Pre-Regular $p$-Open Sets

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

$**gα$ Closed and $**gα$ Open Sets in the Digital Plane

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

C# Application to Deal with Neutrosophic $g \alpha$-Closed Sets in Neutrosophic Topology

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

Point-Free Topological Monoids and Hopf Algebras on Locales and Frames

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] submitted on 2020-01-18 18:45:19

Strip Configuration of the Poincare' Sphere

Authors: Vincenzo Nardozza
Comments: 3 Pages.

In this paper we find and discuss the Strip Configuration of the Poincare' Sphere.
Category: Topology

[18] viXra:2001.0311 [pdf] submitted on 2020-01-16 17:12:53

On Some New Notions in Nano Ideal Topological Spaces

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

Preopen Sets in Ideal Generalized Topological Spaces

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

On I-Open Sets and I-Continuous Functions in Ideal Bitopological Spaces

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

Separation Axioms in Ideal Bitopological Spaces

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

Properties of $\alpha$-Open Sets in Ideal Minimal Spaces

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

Properties of $\beta$-Open Sets in Ideal Minimal Spaces

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

On Upper and Lower Slightly $\delta$-$\beta$-Continuous Multifunctions

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

Properties of Ideal Bitopological $\alpha$-Open Sets

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

On New Separation Axioms in Bitopological Spaces

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

On qi-Open Sets in Ideal Bitopological Spaces

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

Semiopen Sets in Ideal Bitopological Spaces

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

Some Remarks on Low Separation Axioms Via id-Sets

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

Some Fundamental Properties of $\beta$-Open Sets in Ideal Bitopological Spaces

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

Semiopen Sets in Ideal Minimal Spaces

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

On I-Open Sets and I-Continuous Functions in Ideal Minimal Spaces

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] submitted on 2020-01-09 14:45:39

A Remark on the Erd\'{o}s-Ulam Problem

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

[2] viXra:2001.0094 [pdf] submitted on 2020-01-06 16:13:55

On a Connected $T_{1/2}$ Alexandroff Topology and $^*g\hat{\alpha}$-Closed Sets in Digital Plane

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

Topologies on $Z^{n}$ that Are not Homeomorphic to the N-Dimensional Khalimsky Topological Space

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