Partitions of compact Hausdorff spaces
Volume 142 / 1993
Fundamenta Mathematicae 142 (1993), 89-100
DOI: 10.4064/fm-142-1-89-100
Abstract
Under the assumption that the real line cannot be covered by $ω_1$-many nowhere dense sets, it is shown that (a) no Čech-complete space can be partitioned into $ω_1$-many closed nowhere dense sets; (b) no Hausdorff continuum can be partitioned into $ω_1$-many closed sets; and (c) no compact Hausdorff space can be partitioned into $ω_1$-many closed $G_δ$-sets.
