On θ_α-closed Sets, θ_α-continuity and α-almost Compactness for Crisp Subsets in A Fuzzy Topological Space

摘要

This paper is a continuation of the study of α-almost compactness for crisp subsets in a fuzzy topological space, initiated in [5] in terms of the notion of α-shading of Gantner et al. [4]. A class of ordinary subsets, called θ_α-closed sets, which inherit α-almost compactness of a spece X (endowed with a fuzzy topology) is introduced and studied. Incidentally, we require to introduce another class of sets containing that of θ_α-closed sets. Two types of mutually independent functions between two fuzzy topological spaces are also defined and it is shown that α-almost compactness of crisp subsets remains invariant under each of these maps.