Local fuzzy compactness with respect to fuzzy ideal

Abstract

Given a nonempty set X, a fuzzy ideal I on X is a collection of subsets of X closed under finite union and subset operations. In this paper we define a space to be locally I fuzzy compact space if every point in the space has an I fuzzy compact neighbourhood. Basic results concerning locally I fuzzy compact spaces are given relating to subspaces, preservation of functions, and products. Classical results concerning locally fuzzy compact spaces are obtained by I ={φ},and certain results for locally H-closed spaces are obtained by letting I be the fuzzy ideal of nowhere dense sets. Locally H-closed spaces are characterized in the category of Hausdorff spaces as being the locally nowhere-dense-fuzzy compact sets.