Some separation axioms in fuzzy soft bitopological spaces

Abstract

It is known that separation axioms are playing a vital role in study of topological spaces. In this paper, Some Separation axioms have been studied in context of fuzzy soft bitopological spaces. we introduce and study the notions of pairwise fuzzy soft $T_{i}$-spaces; $(i =0, 1, 2)$. This study focuses on question: If a fuzzy soft bitopological space $(X, E, \tau_{1}, \tau_{2})$ is a pairwise fuzzy soft $T_{i}$-space; $(i =0, 1, 2)$, what can be said about the following situations:

(1) both $(X, E, \tau_{1})$ and $(X, E, \tau_{2})$ are fuzzy soft $T_{i}$-spaces; $(i =0, 1, 2)$,

(2) $(X, E,\tau_{12})$ is a supra fuzzy soft $T_{i}$-space; $(i =0, 1, 2)$.

(3) fuzzy soft subspaces $(X, E,\tau_{1_{Y}}, \tau_{2_{Y}})$ are fuzzy soft $T_{i}$-spaces for $ \phi \neq Y \subset X$; $(i =0, 1, 2)$. Finally, characterizations theorem is proved for pairwise fuzzy soft Hausdorff space.