In this paper we introduce the notion of supra soft topological spaces. We extend the notion of -operation, pre-open soft sets, -open soft sets, semi-open soft sets and -open soft sets to such spaces and study their properties and the relations between them. Also, we introduce the concepts of supra pre (resp. -, semi-, -) continuous soft functions on these spaces and study some of their properties. We show that a mapping between two soft topological spaces is supra -continuous soft if and only if it is supra pre-continuous soft and supra semi-continuous soft. The importance of this approach is that, the class of supra soft topological spaces is wider and more general than the class of soft topological spaces.

Abstract:The purpose of this paper is to introduce the notion of soft ideal in soft set theory. The concept of soft local function is also introduced. These concepts are discussed with a view to find new soft topologies from the original one. The basic structure, especially a basis for such generated soft topologies also studied here. Finally, the notion of compatibility of soft ideals with soft topologies is introduced and some equivalent conditions concerning this topic are established here.

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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.