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Compactness in \(L\)-fuzzy topological spaces. (English) Zbl 1260.54019

Summary: The aim of this paper is to introduce a new notion of \(L\)-fuzzy compactness in \(L\)-fuzzy topological spaces, which is a generalization of Lowen’s fuzzy compactness in \(L\)-topological spaces. The union of two \(L\)-fuzzy compact \(L\)-sets is \(L\)-fuzzy compact. The intersection of an \(L\)-fuzzy compact \(L\)-set \(G\) and an \(L\)-set \(H\) with \({\mathcal T}^*(H)=\top\) is \(L\)-fuzzy compact. The \(L\)-fuzzy continuous image of an \(L\)-fuzzy compact \(L\)-set is \(L\)-fuzzy compact. The Tychonoff Theorem for \(L\)-fuzzy compactness is true.

MSC:

54A40 Fuzzy topology
03E72 Theory of fuzzy sets, etc.
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