Partial soft separation axioms and soft compact spaces

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 [22], and third, to obtain a relation-
ship between soft Hausdorff and new soft regular spaces similar to those exists on 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 T i -spaces (i = 0,1,2,3,4), depending on a totally 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 T i -spaces are stronger than soft T i -spaces, for i = 0,1,4. Also, we define a p-soft regular space, which is weaker than a soft regular space and verify the equivalent between soft T 2 -spaces and p-soft T 3 -spaces when the universe set is finite. In the last section, we show the relationships between some p-soft T i -spaces and soft compact spaces, and in particular, we conclude under what conditions
a soft subset of a p-soft T 2 -space is soft compact and prove that every soft compact p-soft T 2 -space is soft T 3 -space. Finally, we illuminate that some findings obtained in general topology are not true
concerning soft topological spaces such as a finite soft topological space need not be soft compact.