A new notion of fuzzy compactness in \(L\)-topological spaces. (English) Zbl 1080.54004

Considering \(L\) a completely distributive de Morgan algebra, the author introduces a notion of fuzzy compactness in \(L\)-topological spaces called \(S^*\)-compactness. He compares various notions of fuzzy compactness introduced over the years by various authors. Besides giving basic facts, the Tychonoff theorem for \(S^*\)-compactness is obtained and it is shown that the \(L\)-fuzzy unit interval \(I(L)\) is \(S^*\)-compact. Characterizations of \(S^*\)-compactness by nets are provided.


54A40 Fuzzy topology
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