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, 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.
@article{1595,
title = {Connectedness in Fuzzy bitopological Spaces},
journal = {CUBO, A Mathematical Journal},
volume = {9},
year = {2007},
language = {en},
url = {http://dml.mathdoc.fr/item/1595}
}
Gupta, M.K.; Pratap Singh, Rupen. Connectedness in Fuzzy bitopological Spaces. CUBO, A Mathematical Journal, Tome 9 (2007) . http://gdmltest.u-ga.fr/item/1595/