Some Properties of Fuzzy Supra Soft Topological Spaces

Abstract

In this paper, we introduce the notion of fuzzy supra soft topological spaces, which is a generalization to the notion of fuzzy soft topological spaces and supra soft topological spaces. Also, we consider the notion of fuzzy supra soft continuity as a generalization to fuzzy soft continuity, supported by examples and counterexamples. These examples illustrating the notions used in the paper are included. So we can see that all these concepts are independent from each other ordoes implies the other. Finally, as a direct application to fuzzy supra soft topological spaces, we introduce the notion of fuzzy supra soft compact (resp. fuzzy supra soft lindel ̈of) spaces to such spaces as a generalization to fuzzy soft compactness. Furthermore, we establish some interesting properties of this notion.

On characterizations of fuzzy supra soft connected spaces

“…Definition 2.15 [12] Let be a family of fs-sets over a universe . Then is called fuzzy supra soft topology (briefey fsst) on if…”

“…Definition 2.16 [12] Let ( , * , ) be a fsts and ( , , ) be a fssts. We say that is a fsst associated with * if * ⊂ .…”

“…Definition 2.17 [12] Let ( , , ) be a fssts and ∈ ( ) . Then the fuzzy supra soft interior of , denoted by ( ) is defined as…”

“…So, defines a fsst on such that ⊆ and is a fss-disconnected space, since , ∈ and form a fss-separation of 1 . Definition 3.6 [12] Let ( , , ) be a fssts and ⊆ . Let be a fs-set over ( , ) defined by:…”

“…More topological properties to fuzzy soft topological spaces were investigated in [9,10]. As an extension to the notion of supra soft topological spaces [11] and fuzzy soft topological spaces [6,9], Abd El-latif [12] proposed the definition of fuzzy supra soft topological spaces. More topological properties, like fssgeneralized closed (open) sets and fss-almost compact spaces, were investigated in [13].…”