γ-Operation and Some Types of Soft Sets and Soft Continuity of (Supra) Soft Topological Spaces

Abstract

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.

Decomposition of soft continuity via soft locally b-closed set

“…(1) a soft semiopen set [8] in X if (F; E) v cl(int(F; E)), (2) a soft preopen set [6] [12] in X if (F; E) v cl(int(cl(F; E))), (5) a soft regular open set [22] in X if (F; E) = int(cl(F; E)), (6) a soft A-set [21]…”

Supra Soft R-Separation Axioms

“…It got some stability only after the introduction of soft topology in 2011 [13]. In a study, scientist introduced [14,15]. In other research, some researchers introduced the notion of soft semi separation axioms.…”

Soft Semi Compactness via Soft Ideals

“…They also defined and discussed the properties of soft interior, soft exterior and soft boundary which are fundamental for further research on soft topology and will strengthen the foundations of the theory of soft topological spaces. Kandil et al [11] introduced a unification of some types of different kinds of subsets of soft topological spaces using the notions of γ-operation. Kandil et al [14] generalize this unification of some types of different kinds of subsets of soft topological spaces using the notions of γ-operation to supra soft topological spaces.…”