Connectedness in Fuzzy bitopological Spaces
Pratap Singh, Rupen
In this paper, we extend the four notions of connectedness introduced by Ajmal and Kohli  to pairwise connectedness for an arbitrary fuzzy set in fuzzy bitopological spaces (X, τ1, τ2) and discuss the implications that exist between them. These conditions are called сk- pairwise connectedness (k = 1, 2, 3, 4). We establish that the union of an arbitrary family of сk- pairwise connected (k = 1, 2) fuzzy set which are pairwise intersecting is сk- pairwise connected (k = 1, 2). Also the union of arbitrary family of сk- pairwise connected (k = 3, 4) fuzzy set which are overlapping is сk- pairwise connected (k = 3, 4). It is also shown that (τi, τj)- closure of a с1- pairwise connected fuzzy set. We also discuss the preservation of сk- pairwise connectedness (k = 1, 2, 3, 4) under fuzzy pairwise continuous mapping and fuzzy pairwise open mapping.