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Fuzzy compactness via summability

✍ Scribed by Hüseyi̇n Çakalli; Pratulananda Das

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
368 KB
Volume
22
Category
Article
ISSN
0893-9659

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✦ Synopsis

A fuzzy subset α of a fuzzy topological space is fuzzy sequentially compact if any sequence x = (λ xn an ) 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 = (λ xn an ) 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.

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The notion of Q -compact fuzzy topological spaces was ÿrst introduced by Zhongfu (Kexue Tongbao 29(5) (1984) 582-585). In this paper we extend this notion to fuzzy supra topological spaces and study some of their properties. We also introduce the notion of fuzzy Q -almost compact (Q -almost supracom