Abstract:It is well-known that compacta (i.e.\ compact Hausdorff spaces) are maximally resolvable, that is every compactum $X$ contains $\Delta(X)$ many pairwise disjoint dense subsets, where $\Delta(X)$ denotes the minimum size of a non-empty open set in $X$. The aim of this note is to prove the following analogous result: Every compactum $X$ contains $\Delta_\delta(X)$ many pairwise disjoint $G_\delta$-dense subsets, where $\Delta_\delta(X)$ denotes the minimum size of a non-empty $G_\delta$ set in~$X$.
Keywords: compact spaces, $G_\delta $-sets, resolvability
AMS Subject Classification: 54A25 54D30 03E10