RELATIVE COMPACTNESS AND COMPACTNESS OF GENERAL SUBSETS IN AN I- TOPOLOGICAL SPACE

Abstract

In a previous work, we introduced a form of compactness applicable to general fuzzy sets in an I-topological space. It was shown that many of the standard results for compactness in general topology remain valid in the fuzzy setting. In this paper we continue our investigations into the behaviour of compact fuzzy subsets. We also introduce the notion of a relatively compact fuzzy subset and obtain results very similar to those of general topology. Many of our results are in the setting of fuzzy neighbourhood space and fuzzy uniform spaces. In particular, a number of criteria for compactness, already known for the whole space, are extended to arbitrary fuzzy subsets in a fuzzy neighbourhood space.