Elsevier

Applied Mathematics Letters

Volume 22, Issue 11, November 2009, Pages 1665-1669
Applied Mathematics Letters

Fuzzy compactness via summability

https://doi.org/10.1016/j.aml.2009.05.015Get rights and content
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Abstract

A fuzzy subset α of a fuzzy topological space is fuzzy sequentially compact if any sequence x=(λanxn) of fuzzy points in α has a generalized fuzzy subsequence which is fuzzy convergent in α. More generally we say that a fuzzy subset α of a fuzzy topological space X is G-fuzzy sequentially compact if any sequence x=(λanxn) of fuzzy points in α has a generalized fuzzy subsequence y such that G(y)α where G is a function from a suitable subset of the set of all sequences of fuzzy points in X. We investigate some of the basic properties of this compactness and suggest some open problems.

Keywords

Fuzzy point
Fuzzy convergence
G-Fuzzy sequentially closed
G-Fuzzy sequential compactness

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