Abstract

This paper deals with a new type of compactness, viz., fuzzy pre $\beta$-compactness by using fuzzy pre $\beta$-open set [1] as a basic tool. We characterize this newly defined compactness by fuzzy net and prefilterbase. It is shown that this compactness implies fuzzy almost compactness [3] and the converse is true only on fuzzy pre $\beta$-regular space [1]. Afterwards, it is shown that this compactness remains invariant under fuzzy pre $\beta$-irresolute function [1].

Keywords and Phrases

Fuzzy pre $\beta$-open set, fuzzy pre $\beta$-regular space, fuzzy regularly pre $\beta$-closed set, fuzzy pre $\beta$-compact set (space), pre $\beta$-adherent point of a prefilterbase, pre $\beta$-cluster point of a fuzzy net.

A.M.S. subject classification

54A40, 03E72.

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