Connectedness in Fuzzy bitopological Spaces
- M.K. Gupta r_p_rp@rediffmail.com
- Rupen Pratap Singh r_p_rp@dediffmail.com
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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 Ñk- pairwise connectedness (k = 1, 2, 3, 4). We establish that the union of an arbitrary family of Ñk- pairwise connected (k = 1, 2) fuzzy set which are pairwise intersecting is Ñk- pairwise connected (k = 1, 2). Also the union of arbitrary family of Ñk- pairwise connected (k = 3, 4) fuzzy set which are overlapping is Ñk- 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 Ñk- pairwise connectedness (k = 1, 2, 3, 4) under fuzzy pairwise continuous mapping and fuzzy pairwise open mapping.