On compactness in bifuzzy topological spaces

Abstract

Compactness in a bifuzzy topological space has been studied earlier by Abd El-Monsef and Ramadan (Fuzzy Sets and Systems, 30, 1989, 165-174) and Safiya et al. (Fuzzy Sets and Systems, 62, 1994, 89-96) as generalizations of P-compactness or S-compactness in a bitopological space. In Section 2 of this note, we have obtained some interesting results related to PC-compactness introduced by Safiya et al. (Fuzzy Sets and Systems, 62, 1994, 89-96) as a concept parallelling that of P-compactness of bitopological spaces. Further, in Section 3, we have introduced and studied B-compactness, B-α compactness in a bifuzzy topological space which are parallel to the notion of B-compactness in a bitopological space. We have also defied B-almost (B-α-almost) compactness in a bfts which is weaker than B-compactness (B-α-compactness). Several related results have been proved. © 2001 Elsevier Science B.V.