Lowen's compactness in \(L\)-fuzzy topological spaces
type: Item
instance of: scholarly article
title: Lowen's compactness in \(L\)-fuzzy topological spaces
zbMATH Open document ID: 0787.54008
DOI: 10.1016/0165-0114(93)90404-6
author: Guangwu Meng
published in: Fuzzy Sets and Systems
publication date: 1994-05-24T00:00:00Z
review text: \textit{R. Lowen's} concept of compactness of a fuzzy topological space [J. Math. Anal. Appl. 56, 621-633 (1976; Zbl 0342.54003)] was extended by \textit{Wang Goujun} [Shanxi Normal Univ. Press, Xi'an, China, 1988 (in Chinese)] to the case of \(L\)-fuzzy topological spaces where \(L\) is a completely distributive complete bounded lattice with an order-reversing involution. In this extension \(\vee\)-irreducible non-zero elements of \(L\) (so-called molecules of \(L\)) play a crucial role. In this paper some new characterizations of Lowen's compactness of \(L\)- fuzzy topological spaces are obtained. Among them characterizations by families of remote neighbourhoods, by \(\alpha\)-filters and by families of \(L\)-fuzzy sets with finite \(\alpha\)-intersection property (here \(\alpha\) is a molecule in \(L\)). Besides it is proved that a topological space \((X,T)\) is compact iff the fuzzy topological space \((L^ X,\omega(T))\) is Lowen's compact, where \(\omega(T)\) denotes the family of all mappings \(U: (X,T) \to L\) such that all \(\{x: U(x) \leq a\}\), \(a\in L\), are closed in \((X,T)\).
Mathematics Subject Classification ID: 54A40
zbMATH DE Number: 487477
zbMATH Keywords: molecule
zbMATH Keywords: alpha-filter
zbMATH Keywords: Lowen's compactness
reviewed by: Alexander Šostak
MaRDI profile type: Publication
full work available at URL: 0165-0114(93)90404-6
OpenAlex ID: W2004604759
cites work: Fuzzy topological spaces and fuzzy compactness
cites work: A new fuzzy compactness defined by fuzzy nets
cites work: The N-compactness in L-fuzzy topological spaces
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description: scientific article; zbMATH DE number 487477