Connectedness in Fuzzy bitopological Spaces

Abstract

In this paper, we extend the four notions of connectedness introduced by Ajmal and Kohli [1] to pairwise connectedness for an arbitrary fuzzy set in fuzzy bitopological spaces (X, Ï„₁, Ï„₂) and discuss the implications that exist between them. These conditions are called Ñ_k- pairwise connectedness (k = 1, 2, 3, 4). We establish that the union of an arbitrary family of Ñ_k- pairwise connected (k = 1, 2) fuzzy set which are pairwise intersecting is Ñ_k- pairwise connected (k = 1, 2). Also the union of arbitrary family of Ñ_k- pairwise connected (k = 3, 4) fuzzy set which are overlapping is Ñ_k- pairwise connected (k = 3, 4). It is also shown that (Ï„_i, Ï„_j)- closure of a Ñ₁- pairwise connected fuzzy set. We also discuss the preservation of  Ñ_k- pairwise connectedness (k = 1, 2, 3, 4) under fuzzy pairwise continuous mapping and fuzzy pairwise open mapping.