The cardinal functions on \(L\)-fuzzy topological spaces
Basic cardinal functions on topological spaces and relations between these functions are of a steady interest of topologists for many years. The author of the present paper defines counterparts of some cardinal functions for \(L\)-fuzzy topological spaces (where \(L\) is a completely distributive lattice) and studies basic properties of these functions and relations between them. For example, it is proved that for any \(L\)-fuzzy topological space \(X\) \(c(X) \leq\min (d(X)\), \(s(X))\), where \(c(X)\), \(d(X)\), and \(s(X)\) are, respectively, ``cellularity'', ``density'' and ``spread'' of \(X\). Let us note that the author develops his theory in the spirit of \textit{Wang Guojun}'s approach [ibid. 47, No. 3, 351-376 (1992; Zbl 0783.54032)]. In particular, such concepts as `` a molecule'' (= an \(\vee\)-irreducible element) and ``a remote neighbourhood'' are intensely used here. Notice also that basic cardinal functions for fuzzy topological spaces were earlier introduced and studied in the reviewer's paper [\textit{A. Šostak}, Rad. Mat. 6, No. 2, 249-263 (1990; Zbl 0718.54016)]. However, the context of the reviewer's paper is restricted to the case \(L=[0,1]\).
scientific article; zbMATH DE number 1274662