ON SEVERAL TYPES OF COMPACTNESS IN SMOOTH TOPOLOGICAL-SPACES

The smooth closure and smooth interior of a fuzzy set w.r.t. a smooth topology were defined by Gayyar et al. (1994), and some relations betw een a few types of compactness were established in the presence of str ong restrictions. In this paper, by constructing new definitions of sm ooth closure and smooth interior which have more desirable properties than those of Gayyar et al. (1994), we prove that several hypothesis i n the results of Gayyar et al. (1994) can be weakened and show that th e relations which hold between various types of compactness in fuzzy t opological spaces in Chang's sense (CFTS for short) (Di Concilio and G erla, 1984; Haydar Es, 1987) can be extended to smooth topological spa ces. (C) 1997 Published by Elsevier Science B.V.