Fuzzy topology. II. Product and quotient spaces

Abstract

In [6], after introducing the fundamental concepts of fuzzy points which take crisp singletons or ordinary points as special cases, q-relations and Q-neighborhoods of fuzzy points, we built up a satisfactory theory of neighborhood structures and generalized many fundamental notions and theorems, especially those theorems in the theory of Moore-Smith’s convergence such as those contained in [5, Chaps. I, II]. The purpose of the present paper is to generalize all the ehtorems concerning product spaces and quotient spaces contained in [5, Chap. III]..Our treatment will sharpen the related results contained in the literature [l-4] so that these problems in fuzzy topology will be solved to the same degree as the corresponding ones in general topology. The present work is the continuation of [6] and hence all the conventions in [6] still hold good in the present paper, especially that (X, r) and (Y, %) d enote fuzzy topological spaces.