On Binary Soft Topological Spaces

Abstract

In the present paper, we introduce binary soft topological spaces which are defined over two initial universe sets with a fixed set of parameters. The notions of binary soft open sets, binary soft closed sets, binary soft closure, binary soft interior, binary soft boundary, binary soft neighborhood of a point are introduced and their basic properties are investigated with the suitable examples. These results are fundamental for further research on binary soft topology and will strengthen the foundations of the theory of binary soft topological spaces.

Binary Bipolar Soft Points and Topology on Binary Bipolar Soft Sets with Their Symmetric Properties

“…Correspondingly, in 2016, the concept of the binary soft set was first defined by Açıkgöz and Taş in [24], where they introduced the binary soft set on two initial universal sets and proposed some of their properties. After that, Benchalli et al [25] presented some related basic properties, which are defined over two initial universal sets with suitable parameters, and they defined the binary soft topological spaces with some of their properties. Recently, in 2023, Naime and Orhan [26] defined a new concept of bipolar soft sets over two universal sets and a parameter set, namely binary bipolar soft sets, which is an extension of bipolar soft sets and binary soft sets.…”

Binary soft locally closed sets

“…In 2017, Benchalli et al [2] coined the concept of binary soft topological spaces and stated the definition of binary soft topology as, a collection τ of binary soft subsets over U 1 , U 2 is a binary soft topology over U 1 , U 2 if ∅, ρ ∈ τ and τ is closed under arbitrary union and finite intersection of binary soft sets. The members of τ are binary soft open sets and their family is denoted by BSO(U 1 , U 2 ).…”

“…The complements of binary soft open sets are binary soft closed sets, and the structure (U 1 , U 2 , τ, ρ) is a binary soft topological space. Also the notions of binary soft interior and binary soft closure of binary soft sets are introduced by [2]. Let (A, ρ) be a binary soft subset in (U 1 , U 2 , τ, ρ), then:…”

Application of Soft P-Open Set to Binary Soft Structures

“…In prolongation, a group researcher planned the idea of binary soft topology and linked fundamental properties which are defined over two master sets with appropriate parameters [4]. Other researchers threw their detailed discussion on Binary Soft Topological [5]. Dr. A. Kalaichelvi and P.H.…”