[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]**
*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

[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]**
*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

[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