Soft Pre Separation Axioms and Function with Soft Pre Closed Graph

Abstract

Several notions on soft topology are studied and their basic properties are investigated by using the concept of soft pre open sets and soft pre closure operator which are derived from the basics of soft set theory established by Molodtsov [1]. In this paper we introduce some soft separation axioms called Soft pre R0 and soft pre R1 in soft topological spaces which are defined over an initial universe with a fixed set of parameters. Many characterizations and properties of these spaces have been demonstrated. Necessary and sufficient conditions for a soft topological space to be a soft pre Ri space for i = 0, 1 were also presented. Furthermore, the concept of functions with soft pre closed graph and soft pre cluster set are defined. Many results on these two concepts are proved. Also, it is proved that a function has a soft pre closed graph if and only if its soft pre cluster set is degenerate.