On \(L\)-smooth paracompactness
Patterned after the definition of compactness for \(L\)-subsets of an \(L\)-fuzzy (or \(L\)-smooth) topological space \((X,\tau)\) (in the sense of [\textit{A. P. Šostak}, Rend. Circ. Mat. Palermo, II. Ser. Suppl. 11, 89-103 (1985; Zbl 0638.54007)]), the authors introduce the notion of paracompactness. In case \(\tau\) is a Chang-Goguen \(L\)-topology (i.e. \(\tau:L^X \to\{0,1\})\) this definition reduces to the definition of paracompactness given in [\textit{S. R. T. Kudri}, Fuzzy Sets Syst. 70, No. 1, 119-123 (1995; Zbl 0843.54011)]. Some properties of paracompact \(L\)-subsets of \(L\)-fuzzy topological spaces are studied. In particular, it is proved that paracompactness is inherited by those \(L\)-subsets of \(L\)-fuzzy topological spaces, whose degree of closedness is 1. An (ordinary) topological space \((X,T)\) is paracompact iff the \(L\)-fuzzy topological space \((X,W(T))\), where \(W(T)(f)= \bigvee\{\alpha \in L\mid f\in L^X\) is \(\alpha\)-Scott continuous\} [\textit{H. Aygün}, \textit{M. W. Warner}, \textit{S. R. T. Kudri}, J. Fuzzy Math. 5, No. 2, 321-338 (1997; Zbl 0880.54008)] is paracompact.
scientific article; zbMATH DE number 1660537