Resolvability and complete accumulation points (Q6057444)

The author proves a succinct result on resolvability of topological spaces: if \(X\) is regular and \(\kappa\) is a cardinal such that \(X\) is \(\operatorname{cf}\kappa\)-compact and such that \(\vert X\vert =\Delta(X)=\kappa\) then \(X\) is maximally resolvable.\par The relevant notions are defined as follows: \(\lambda\)-compactness means that every subset of cardinality \(\lambda\) has a complete accumulation point and \(\Delta(X)\) is the dispersion character of \(X\): the minimum cardinality of an open subset of \(X\). Maximal resolvability means that \(X\) has a pairwise disjoint family of \(\vert X\vert \) many dense subsets.\par The paper's introduction gives a nice overview of the history of the problem of maximal resolvability.