Partitions of compact Hausdorff spaces

Volume 142 / 1993

Gary Gruenhage 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.

Authors

  • Gary Gruenhage

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