Fuzzy compactness via summability
A fuzzy subset alpha of a fuzzy topological space is fuzzy sequentially compact if any sequence x = (lambda(chi n)(an)) of fuzzy points in alpha has a generalized fuzzy subsequence which is fuzzy convergent in alpha. More generally we say that a fuzzy subset alpha of a fuzzy topological space X is G-fuzzy sequentially compact if any sequence x = (lambda(chi n)(an)) of fuzzy points in alpha has a generalized fuzzy subsequence y such that G(y) is an element of alpha or 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. (C) 2009 Elsevier Ltd. All rights reserved.
SourceAPPLIED MATHEMATICS LETTERS
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