α-PRECOMPACT SPACE IN FUZZY TOPOLOGICAL SPACE

Anjana Bhattacharyya

doi:10.56827/JRSMMS.2023.1101.10

Anjana Bhattacharyya Department of Mathematics Victoria Institution (College), 78 B, A.P.C. Road, Kolkata- 700009, INDIA

DOI: https://doi.org/10.56827/JRSMMS.2023.1101.10

Keywords: Fuzzy α-preopen set, fuzzy α-preregular space, fuzzy regularly α-preclosed set, fuzzy α-precompact set (space), α-preadherent point of a prefilterbase, α-precluster point of a fuzzy net.

Abstract

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