Some types of pairwise soft sets and the associated soft topologies

Abstract

In this paper, we introduce the notions of pairwise soft sub kernel, and pairwise ∨-soft sets in a soft bitopological space (X, η₁, η₂, E). Also, we study the fundamental properties of pairwise ∨-soft sets and we investigate the associated soft topology η_p∨. Moreover, we introduce the notions of generalized pairwise Λ(∨)-soft sets and we investigate their basic properties. Also, we define a soft closure operator on the family of all generalized pairwise Λ-soft sets and generate, in usual manner, an Alexandroff soft topology η _gpΛ on X which is finer than η_p∨. Furthermore, we prove that (X, η _gpΛ , E) is always a soft $T_{\frac{1}{2}}$ space. In addition, we introduce characterizations of pairwise soft $T_{\frac{1}{2}}^{*}$ by using generalized pairwise Λ-soft sets and we show that the concepts of generalized pairwise Λ-soft set and generalized pairwise closed soft set are independent.