Geodesic
Partitions of compact Hausdorff spaces
Fundamenta Mathematicae, Tome 142 (1993) no. 1, pp. 89-100

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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.
DOI : 10.4064/fm-142-1-89-100

Gary Gruenhage 1

1 
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Gary Gruenhage. Partitions of compact Hausdorff spaces. Fundamenta Mathematicae, Tome 142 (1993) no. 1, pp. 89-100. doi: 10.4064/fm-142-1-89-100

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