Shi, Fu-Gui; Li, Run-Xiang Compactness in \(L\)-fuzzy topological spaces. (English) Zbl 1260.54019 Hacet. J. Math. Stat. 40, No. 6, 767-774 (2011). 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. Cited in 2 Documents MSC: 54A40 Fuzzy topology 03E72 Theory of fuzzy sets, etc. Keywords:\(L\)-fuzzy topology; \(\alpha\)-fuzzy compactness; \(L\)-fuzzy compactness PDFBibTeX XMLCite \textit{F.-G. Shi} and \textit{R.-X. Li}, Hacet. J. Math. Stat. 40, No. 6, 767--774 (2011; Zbl 1260.54019)