Abstract

In this paper we introduce and study a new type of compactness, viz., fuzzy $\alpha$-precompactness by using fuzzy $\alpha$-preopen set [1] as a basic tool. Here we also characterize this space by fuzzy net and prefilterbase. We have shown that fuzzy $\alpha$-precompactness implies fuzzy almost compactness [4] and the converse is true only on fuzzy $\alpha$-preregular space [1]. 

Keywords and Phrases

Fuzzy $\alpha$-preopen set, fuzzy $\alpha$-preregular space, fuzzy regularly $\alpha$-preclosed set, fuzzy $\alpha$-precompact set (space), $\alpha$-preadherent point of a prefilterbase, $\alpha$-precluster point of a fuzzy net.

A.M.S. subject classification

54A40, 03E72.

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