scholarly journals New soft separation axioms and fixed soft points with respect to total belong and total non-belong relations

2021 ◽  
Vol 54 (1) ◽  
pp. 196-211
Author(s):  
Tareq M. Al-shami ◽  
Adnan Tercan ◽  
Abdelwaheb Mhemdi
Keyword(s):  
Regular Space ◽  
Topological Spaces ◽  
Separation Axioms ◽  
Constant Shape ◽  
Soft Point

Abstract In this article, we exploit the relations of total belong and total non-belong to introduce new soft separation axioms with respect to ordinary points, namely t t tt -soft pre T i ( i = 0 , 1 , 2 , 3 , 4 ) {T}_{i}\hspace{0.33em}\left(i=0,1,2,3,4) and t t tt -soft pre-regular spaces. The motivations to use these relations are, first, cancel the constant shape of soft pre-open and pre-closed subsets of soft pre-regular spaces, and second, generalization of existing comparable properties on classical topology. With the help of examples, we show the relationships between them as well as with soft pre T i ( i = 0 , 1 , 2 , 3 , 4 ) {T}_{i}\hspace{0.33em}\left(i=0,1,2,3,4) and soft pre-regular spaces. Also, we explain the role of soft hyperconnected and extended soft topological spaces in obtaining some interesting results. We characterize a t t tt -soft pre-regular space and demonstrate that it guarantees the equivalence of t t tt -soft pre T i ( i = 0 , 1 , 2 ) {T}_{i}\hspace{0.33em}\left(i=0,1,2) . Furthermore, we investigate the behaviors of these soft separation axioms with the concepts of product and sum of soft spaces. Finally, we introduce a concept of pre-fixed soft point and study its main properties.

scholarly journals Intuitionistic Fuzzy Topological Spaces Model

2020 ◽  
Vol 55 (2) ◽  
Author(s):  
Hind Fadhil Abbas
Keyword(s):  
Hausdorff Space ◽  
Basic Structure ◽  
Normal Space ◽  
Regular Space ◽  
Topological Spaces ◽  
Intuitionistic Fuzzy ◽  
Separation Axioms ◽  
Fuzzy Ideal ◽  
Scientific Phenomenon ◽  
Fuzzy Topological Spaces

The fusion of technology and science is a very complex and scientific phenomenon that still carries mysteries that need to be understood. To unravel these phenomena, mathematical models are beneficial to treat different systems with unpredictable system elements. Here, the generalized intuitionistic fuzzy ideal is studied with topological space. These concepts are useful to analyze new generalized intuitionistic models. The basic structure is studied here with various relations between the generalized intuitionistic fuzzy ideals and the generalized intuitionistic fuzzy topologies. This study includes intuitionistic fuzzy topological spaces (IFS); the fundamental definitions of intuitionistic fuzzy Hausdorff space; intuitionistic fuzzy regular space; intuitionistic fuzzy normal space; intuitionistic fuzzy continuity; operations on IFS, the compactness and separation axioms.

scholarly journals A Class of Separation Axioms in Generalized Topology

2016 ◽  
Vol 4 (2) ◽  
pp. 151-159
Author(s):  
D Anabalan ◽  
Santhi C
Keyword(s):  
Topological Space ◽  
Generalized Topology ◽  
Regular Space ◽  
Topological Spaces ◽  
Closed Sets ◽  
New Class ◽  
Separation Axioms ◽  
Generalized Topological Space

The purpose of this paper is to introduce and study some new class of definitions like µ-point closure and gµ –regular space concerning generalized topological space. We obtain some characterizations and several properties of such definitions. This paper takes some investigations on generalized topological spaces with gµ –closed sets and gµ–closed sets.

scholarly journals Separation Axioms Interval-Valued Fuzzy Soft Topology via Quasi-Neighbourhood Structure

2019 ◽  
Author(s):  
Mabruka Ali ◽  
Adem Kılıçman ◽  
Azadeh Zahedi Khameneh
Keyword(s):  
Topological Spaces ◽  
Basic Properties ◽  
Soft Topology ◽  
Separation Axioms ◽  
Neighbourhood Structure ◽  
Soft Point ◽  
Interval Valued

In this study, we present the concept of interval-valued fuzzy soft point and then introduce the notions of neighborhood and quasi-neighbourhood of it in interval-valued fuzzy soft topological spaces. Separation axioms in interval-valued fuzzy soft topology, so-called $q$-$T_{i}$ for $ i=0,1,2,3,4 ,$ is introduced and some of its basic properties are also studied.

scholarly journals Characterization of Soft S-Open Sets in Bi-Soft Topological Structure Concerning Crisp Points

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2100
Author(s):  
Arif Mehmood ◽  
Mohammed M. Al-Shomrani ◽  
Muhammad Asad Zaighum ◽  
Saleem Abdullah
Keyword(s):  
Coordinate Space ◽  
Regular Space ◽  
Topological Spaces ◽  
Finite Intersection ◽  
Open Set ◽  
Separation Axioms ◽  
Finite Intersection Property ◽  
Almost All ◽  
Bitopological Spaces

In this article, a soft s-open set in soft bitopological structures is introduced. With the help of this newly defined soft s-open set, soft separation axioms are regenerated in soft bitopological structures with respect to crisp points. Soft continuity at some certain points, soft bases, soft subbase, soft homeomorphism, soft first-countable and soft second-countable, soft connected, soft disconnected and soft locally connected spaces are defined with respect to crisp points under s-open sets in soft bitopological spaces. The product of two soft  axioms with respect crisp points with almost all possibilities in soft bitopological spaces relative to semiopen sets are introduced. In addition to this, soft (countability, base, subbase, finite intersection property, continuity) are addressed with respect to semiopen sets in soft bitopological spaces. Product of soft first and second coordinate spaces are addressed with respect to semiopen sets in soft bitopological spaces. The characterization of soft separation axioms with soft connectedness is addressed with respect to semiopen sets in soft bitopological spaces. In addition to this, the product of two soft topological spaces is (  space if each coordinate space is soft  space, product of two sot topological spaces is (S regular and C regular) space if each coordinate space is (S regular and C regular), the product of two soft topological spaces is connected if each coordinate space is soft connected and the product of two soft topological spaces is (first-countable, second-countable) if each coordinate space is (first countable, second-countable).

scholarly journals Partial soft separation axioms and soft compact spaces

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4755-4771 ◽  
Author(s):  
M.E. El-Shafei ◽  
M. Abo-Elhamayel ◽  
T.M. Al-Shami
Keyword(s):  
Topological Space ◽  
General Topology ◽  
Regular Space ◽  
Topological Spaces ◽  
Finite Product ◽  
Compact Spaces ◽  
Separation Axioms ◽  
Soft Topological Space

The main aim of the present paper is to define new soft separation axioms which lead us, first, to generalize existing comparable properties via general topology, second, to eliminate restrictions on the shape of soft open sets on soft regular spaces which given in [22], and third, to obtain a relationship between soft Hausdorff and new soft regular spaces similar to those exists via general topology. To this end, we define partial belong and total non belong relations, and investigate many properties related to these two relations. We then introduce new soft separation axioms, namely p-soft Ti-spaces (i = 0,1,2,3,4), depending on a total non belong relation, and study their features in detail. With the help of examples, we illustrate the relationships among these soft separation axioms and point out that p-soft Ti-spaces are stronger than soft Ti-spaces, for i = 0,1,4. Also, we define a p-soft regular space, which is weaker than a soft regular space and verify that a p-soft regular condition is sufficient for the equivalent among p-soft Ti-spaces, for i = 0,1,2. Furthermore, we prove the equivalent among finite p-soft Ti-spaces, for i = 1,2,3 and derive that a finite product of p-soft Ti-spaces is p-soft Ti, for i = 0,1,2,3,4. In the last section, we show the relationships which associate some p-soft Ti-spaces with soft compactness, and in particular, we conclude under what conditions a soft subset of a p-soft T2-space is soft compact and prove that every soft compact p-soft T2-space is soft T3-space. Finally, we illuminate that some findings obtained in general topology are not true concerning soft topological spaces which among of them a finite soft topological space need not be soft compact.

scholarly journals Separation Axioms of Interval-Valued Fuzzy Soft Topology via Quasi-Neighborhood Structure

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 178
Author(s):  
Mabruka Ali ◽  
Adem Kılıçman ◽  
Azadeh Zahedi Khameneh
Keyword(s):  
Topological Spaces ◽  
Neighborhood Structure ◽  
Basic Properties ◽  
Soft Topology ◽  
Separation Axioms ◽  
Soft Point ◽  
Interval Valued

In this study, we present the concept of the interval-valued fuzzy soft point and then introduce the notions of its neighborhood and quasi-neighborhood in interval-valued fuzzy soft topological spaces. Separation axioms in an interval-valued fuzzy soft topology, so-called q- T i for i = 0 , 1 , 2 , 3 , 4 , are introduced, and some of their basic properties are also studied.

scholarly journals Soft Separation Axioms and Fixed Soft Points Using Soft Semiopen Sets

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
T. M. Al-shami
Keyword(s):  
Vital Role ◽  
General Topology ◽  
Topological Spaces ◽  
Soft Topology ◽  
Separation Axioms ◽  
The Stability ◽  
Soft Point

The importance of soft separation axioms comes from their vital role in classifications of soft spaces, and their interesting properties are studied. This article is devoted to introducing the concepts of t t -soft semi- T i i = 0 , 1 , 2 , 3 , 4 and t t -soft semiregular spaces with respect to ordinary points. We formulate them by utilizing the relations of total belong and total nonbelong. The advantages behind using these relations are, first, generalization of existing comparable properties on general topology and, second, eliminating the stability shape of soft open and closed subsets of soft semiregular spaces. By some examples, we show the relationships between them as well as with soft semi- T i i = 0 , 1 , 2 , 3 , 4 and soft semiregular spaces. Also, we explore under what conditions they are kept between soft topology and its parametric topologies. We characterize a t t -soft semiregular space and demonstrate that it guarantees the equivalence of t t -soft semi- T i i = 0 , 1 , 2 . Further, we investigate some interrelations of them and some soft topological notions such as soft compactness, product soft spaces, and sum of soft topological spaces. Finally, we define a concept of semifixed soft point and study its main properties.

scholarly journals £-Single Valued Extremally Disconnected Ideal Neutrosophic Topological Spaces

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 53
Author(s):  
Fahad Alsharari
Keyword(s):  
Topological Spaces ◽  
Neutrosophic Sets ◽  
Extremally Disconnected ◽  
Fundamental Properties ◽  
Separation Axioms ◽  
New Concepts ◽  
Definition Of

This paper aims to mark out new concepts of r-single valued neutrosophic sets, called r-single valued neutrosophic £-closed and £-open sets. The definition of £-single valued neutrosophic irresolute mapping is provided and its characteristic properties are discussed. Moreover, the concepts of £-single valued neutrosophic extremally disconnected and £-single valued neutrosophic normal spaces are established. As a result, a useful implication diagram between the r-single valued neutrosophic ideal open sets is obtained. Finally, some kinds of separation axioms, namely r-single valued neutrosophic ideal-Ri (r-SVNIRi, for short), where i={0,1,2,3}, and r-single valued neutrosophic ideal-Tj (r-SVNITj, for short), where j={1,2,212,3,4}, are introduced. Some of their characterizations, fundamental properties, and the relations between these notions have been studied.

Higher separation axioms in L-topologically generated -topological spaces

2002 ◽  
Vol 131 (3) ◽  
pp. 315-322 ◽  
Author(s):  
Tomasz Kubiak ◽  
Iraide Mardones-Pérez
Keyword(s):  
Topological Spaces ◽  
Separation Axioms
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