Partial soft separation axioms and soft compact spaces

Mohammed E. El-Shafei · M. Abo-Elhamayel · Tareq M. Al-shami

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Fuzzy and Soft Set Theory Advanced Topology and Set Theory Fixed Point Theorems Analysis

Abstract

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.

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References

1999Soft set theory—First results 2003Soft set theory 2002An application of soft sets in a decision making problem 2009On some new operations in soft set theory 2007Soft sets and soft groups 2011On soft topological spaces 2005The parameterization reduction of soft sets and its applications 2010Soft sets and soft rings

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2019Partial belong relation on soft separation axioms and decision-making problem, two birds with one stone 2020Applications of partial belong and total non-belong relations on soft separation axioms and decision-making problem 2021On Soft Separation Axioms and Their Applications on Decision-Making Problem 2021Compactness on Soft Topological Ordered Spaces and Its Application on the Information System 2020On Two Classes of Soft Sets in Soft Topological Spaces 2020Sum of Soft Topological Spaces

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