Timeline for Is there a homogeneous compactum where non-empty $G_\delta$s have non-empty interior?
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| May 19, 2019 at 18:58 | comment | added | Taras Banakh | A homogeneous compact almost $P$-space has a cover by closed nowhere dense $P$-sets. For examples of such compact (extremally disconnected) spaces, see this paper: arxiv.org/pdf/1809.05799.pdf | |
| May 19, 2019 at 18:56 | comment | added | Taras Banakh | An almost P-space has uncountable cellularity and because of that cannot be homeomorphic to a compact topological group. To see why a countably cellular Tychonoff space $X$ is not almost P, take a maximal disjoint family $\mathcal U$ of open $F_\sigma$-sets in $X$. Because of countable celularity this family is countable and hence $\bigcup \mathcal U$ is an open dense $F_\sigma$-subset and its complement is a nowhere dense closed $G_\delta$-set. | |
| May 11, 2019 at 13:08 | history | edited | YCor | CC BY-SA 4.0 |
added missing assumption
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| May 11, 2019 at 12:17 | history | asked | Santi Spadaro | CC BY-SA 4.0 |