Comparison of different notions of compactness in the fuzzy topological space

Abstract

Various notions of compactness in a fuzzy topological space have been introduced by different authors. The aim of this thesis is to compare them. We find that in a Tâ‚‚ space (in the sense that no fuzzy net converges to two fuzzy points with different supports) all these notions are equivalent for the whole space. Furthermore, for N-compactness and f-compactness (being the only notions that are defined for an arbitrary fuzzy subset) we have equivalence under a stronger condition, namely, a Tâ‚‚ space in the sense that every prime prefilter has an adherence that is non-zero in at most one point