Resolvability of Lindelöf spaces
A topological space \(X\) is called \(\lambda\)-resolvable if it can be represented as the union of \(\lambda\) dense disjoint subsets; 2-resolvable spaces are called simply resolvable. A cardinal number \(\Delta(X)\) is said to be a dispersion character of a space \(X\) if \(\Delta(X)=\min\{|U|:U \text{ open subset of} X\}\). In the paper under review it is proved that every regular Lindelöf space of uncountable dispersion character is resolvable. This is an affirmative answer to a question posed by \textit{V. I. Malykhin} [Math. Notes 64, No.~5, 607--615 (1998); translation from Mat. Zametki 64, No.~5, 701--712 (1998; Zbl 0936.54039)]. Another result is that a hereditarily finally compact space of uncountable dispersion character is \(\omega\)-resolvable. A topological space is called finally compact if any open cover of \(X\) has a countable subcover.
scientific article; zbMATH DE number 5358107