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.
Separation Axioms in Intuitionistic Fuzzy Topological Spaces