Let ( X ,t, E ) be a soft topological space. A mapping ?: SS ( X ) E ? SS ( X ) E is said to be an operation on OS ( X ) if . The collection of all ?-open soft sets is denoted by . Also, the complement of ?-open soft set is called ?-closed soft set, i.e CS (?) = { F E : F E is a ?-open soft set, F E ? SS ( X ) E } is the family of all ?-closed soft sets.
Published in Chapter:
γ-Operation and Some Types of Soft Sets and Soft Continuity of (Supra) Soft Topological Spaces
Ali Kandil (Helwan University, Egypt), Osama A. El-Tantawy (Zagazig University, Egypt), Sobhy A. El-Sheikh (Ain Shams University, Egypt), and A. M. Abd El-latif (Ain Shams University, Egypt)
Copyright: © 2016
|Pages: 45
DOI: 10.4018/978-1-4666-9798-0.ch008
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.