Soft (pre) -expandable spaces

Abstract

Soft set theory is a topic of interest for many researches working in a various of fields. In order to advance this field of study, we invest the soft pre-open sets to introduce a new generalization for soft-expandable, namely soft(pre) -expandable. We used the soft pre-open sets in various locations in the definition of soft-expandable spaces to give either equivalent definitions of soft expandable spaces or to give different types of soft spaces, we will show the connections between them and based on these connections, the definition of soft(pre) -expandable space was chosen. Relationships between this soft topological space with other some know soft topological spaces are examined. Also, we show soft(pre) -expandable and soft expandable are equivalent if the soft topological space is either soft-QSM or ω0-soft(pre) -Compact, and some other features of this spaces with helpful examples are discussed to understand this space more. Finally, we finished this work with our study of two concepts called soft(pre)α - expandable set and soft(pre)β -expandable set.