Abstract
Abstract This paper intends to initiate the study of nearly compact and θ-rigid fuzzy sets in a fuzzy topological space. These two classes of fuzzy sets are seen to be properly contained in the class of fuzzy compact sets and properly contain the class of fuzzy almost compact sets. Several characterizations and certain other properties of these two types of fuzzy sets are established by using the concepts of fuzzy δ-closures and θ-closures of fuzzy sets and fuzzy filterbases.
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