Partitions of compact Hausdorff spaces

Gruenhage, Gary

Gruenhage, Gary

Fundamenta Mathematicae, Tome 142 (1993), p. 89-100 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Publié le : 1993-01-01

Zbl 0814.54015

EUDML-ID : urn:eudml:doc:211974

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     author = {Gary Gruenhage},
     title = {Partitions of compact Hausdorff spaces},
     journal = {Fundamenta Mathematicae},
     volume = {142},
     year = {1993},
     pages = {89-100},
     zbl = {0814.54015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv142i1p89bwm}
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Gruenhage, Gary. Partitions of compact Hausdorff spaces. Fundamenta Mathematicae, Tome 142 (1993) pp. 89-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv142i1p89bwm/

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