scholarly journals Two types of separation axioms on supra soft topological spaces

2019 ◽  
Vol 52 (1) ◽  
pp. 147-165 ◽  
Author(s):  
Tareq M. Al-shami ◽  
Mohammed E. El-Shafei
Keyword(s):  
General Class ◽  
Topological Spaces ◽  
Finite Product ◽  
Soft Sets ◽  
Separation Axioms ◽  
Continuous Mappings ◽  
The Difference

AbstractIn 2011, Shabir and Naz [1] employed the notion of soft sets to introduce the concept of soft topologies; and in 2014, El-Sheikh and Abd El-Latif [2] relaxed the conditions of soft topologies to construct a wider and more general class, namely supra soft topologies. In this disquisition, we continue studying supra soft topologies by presenting two kinds of supra soft separation axioms, namely supra soft Ti-spaces and supra p-soft Ti-spaces for i = 0, 1, 2, 3, 4. These two types are formulated with respect to the ordinary points; and the difference between them is attributed to the applied non belong relations in their definitions.We investigate the relationships between them and their parametric supra topologies; and we provide many examples to separately elucidate the relationships among spaces of each type. Then we elaborate that supra p-soft Ti-spaces are finer than supra soft Ti-spaces in the case of i = 0, 1, 4; and we demonstrate that supra soft T3-spaces are finer than supra p-soft T3-spaces.We point out that supra p-soft Ti-axioms imply supra p-soft Ti−1, however, this characterization does not hold for supra soft Ti-axioms (see, Remark (3.30)). Also, we give a complete description of the concepts of supra p-soft Ti-spaces (i = 1, 2) and supra p-soft regular spaces. Moreover,we define the finite product of supra soft spaces and manifest that the finite product of supra soft Ti (supra p-soft Ti) is supra soft Ti (supra p-soft Ti) for i = 0, 1, 2, 3. After investigating some properties of these axioms in relation with some of the supra soft topological notions such as supra soft subspaces and enriched supra soft topologies, we explore the images of these axioms under soft S*-continuous mappings. Ultimately, we provide an illustrative diagram to show the interrelations between the initiated supra soft spaces.

Connectedness Between Soft Sets

2018 ◽  
Vol 14 (01) ◽  
pp. 53-71 ◽  
Author(s):  
Samajh Singh Thakur ◽  
Alpa Singh Rajput
Keyword(s):  
Soft Set ◽  
Topological Spaces ◽  
Soft Sets ◽  
Continuous Mappings ◽  
Weakly Continuous

In the present paper, the concepts of soft connectedness between soft sets, soft set-connected and soft weakly continuous mappings in soft topological spaces have been introduced and studied.

scholarly journals On Soft Separation Axioms and Their Applications on Decision-Making Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
T. M. Al-shami
Keyword(s):  
Decision Making ◽  
Topological Spaces ◽  
Topological Properties ◽  
Finite Product ◽  
Separation Axioms ◽  
Decision Making Problem ◽  
Weak Structure

In this work, we introduce new types of soft separation axioms called p t -soft α regular and p t -soft α T i -spaces i = 0,1,2,3,4 using partial belong and total nonbelong relations between ordinary points and soft α -open sets. These soft separation axioms enable us to initiate new families of soft spaces and then obtain new interesting properties. We provide several examples to elucidate the relationships between them as well as their relationships with e -soft T i , soft α T i , and t t -soft α T i -spaces. Also, we determine the conditions under which they are equivalent and link them with their counterparts on topological spaces. Furthermore, we prove that p t -soft α T i -spaces i = 0,1,2,3,4 are additive and topological properties and demonstrate that p t -soft α T i -spaces i = 0,1,2 are preserved under finite product of soft spaces. Finally, we discuss an application of optimal choices using the idea of p t -soft T i -spaces i = 0,1,2 on the content of soft weak structure. We provide an algorithm of this application with an example showing how this algorithm is carried out. In fact, this study represents the first investigation of real applications of soft separation axioms.

scholarly journals Some Applications of Supra Preopen Sets

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
M. E. El-Shafei ◽  
A. H. Zakari ◽  
T. M. Al-shami
Keyword(s):  
Topological Spaces ◽  
Difference Property ◽  
Boundary Points ◽  
Separation Axioms ◽  
The Difference

The aim of this work is to define some concepts on supra topological spaces using supra preopen sets and investigate main properties. We started this paper by correcting some results obtained in previous study and presenting further properties of supra preopen sets. Then, we introduce a concept of supra prehomeomorphism maps and discuss its main properties. After that we explore the concepts of supra limit and supra boundary points of a set with respect to supra preopen sets and examine their behaviours on the spaces that possess the difference property. Finally, we formulate the concepts of supra pre-Ti-spaces i=0,1,2,3,4 and give completely descriptions for each one of them. In general, we study their main properties in detail and show the implications of these separation axioms among themselves as well as with STi-space with the help of some interesting examples.

scholarly journals Limit Points and Separation Axioms with Respect to Supra Semi-open Sets

2020 ◽  
Vol 13 (3) ◽  
pp. 427-443 ◽  
Author(s):  
Tareq M. AL-shami ◽  
E. A. Abo-Tabl ◽  
Baravan Assad ◽  
Mohamed Arahet
Keyword(s):  
Real Life ◽  
Research Area ◽  
Topological Spaces ◽  
Difference Property ◽  
Separation Axioms ◽  
Life Problems ◽  
New Concepts ◽  
Limit Points ◽  
The Difference

Sometimes we need to minimize the conditions of topology for different reasons such as obtaining more convenient structures to describe some real-life problems, or constructing some counterexamples whom show the interrelations between certain topological concepts, or preserving some properties under fewer conditions of those on topology. To contribute this research area, in this paper, we establish some new concepts on supra topological spaces using supra semi-open sets and give some characterizations of them. First, we introduce a concept of supra semi limit points of a set and study main properties, in particular, on the spaces that possess the difference property. Second, we define and investigate new separation axioms, namely supra semi Ti-spaces (i = 0, 1, 2, 3, 4) and give complete descriptions for each one of them. We provide some examples to show the relationships between them as well as with STi-space.

scholarly journals is*-Open Sets, is*- Mappings and is*-separation Axioms in Topological Spaces

2019 ◽  
Author(s):  
Omar Khattabomar
Keyword(s):  
Topological Spaces ◽  
New Class ◽  
Open Set ◽  
Separation Axioms ◽  
Continuous Mappings

In this paper, we introduce a new class of open sets that is called is*-open set . Also, we present the notion of is*-continuous, is*-open, is*-irresolute, is*-totally continuous, and is-contra-continuous mappings, and we investigate some properties of these mappings. Furthermore, we introduce some is*-separation axioms, and is*-mappings are related with is*-separation axioms. . .

γ-Operation and Some Types of Soft Sets and Soft Continuity of (Supra) Soft Topological Spaces

2016 ◽  
pp. 127-171
Author(s):  
Ali Kandil ◽  
Osama A. El-Tantawy ◽  
Sobhy A. El-Sheikh ◽  
A. M. Abd El-latif
Keyword(s):  
Topological Space ◽  
Soft Set ◽  
Topological Spaces ◽  
Topological Properties ◽  
Soft Sets ◽  
Soft Mapping ◽  
Separation Axioms ◽  
Different Types

The main purpose of this chapter is to introduce the notions of ?-operation, pre-open soft set a-open sets, semi open soft set and ß-open soft sets to soft topological spaces. We study the relations between these different types of subsets of soft topological spaces. We introduce new soft separation axioms based on the semi open soft sets which are more general than of the open soft sets. We show that the properties of soft semi Ti-spaces (i=1,2) are soft topological properties under the bijection and irresolute open soft mapping. Also, we introduce the notion of supra soft topological spaces. Moreover, we introduce the concept of supra generalized closed soft sets (supra g-closed soft for short) in a supra topological space (X,µ,E) and study their properties in detail.

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 £-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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