Timeline for Possible characterisation of compactly generated weakly Hausdorff spaces
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 5, 2022 at 15:11 | comment | added | user420620 | Compactly generated spaces can be described in terms of the lifting property as $\bigcup(\{\{0\leftrightarrow 1\}\to\{0=1\}\}\cup\{\varnothing \to K \,\,:\,\, K\,\, \text{ compact}\}\big)^{rl}$, see details of the notation at ncatlab.org/nlab/show/lift#ExamplesOfLiftingProperties | |
| Aug 9, 2022 at 9:55 | vote | accept | Peter Kropholler | ||
| Aug 9, 2022 at 9:55 | answer | added | Peter Kropholler | timeline score: 0 | |
| Aug 9, 2022 at 9:46 | comment | added | Peter Scholze | The correct characterization is that they are the topological spaces that can be written as filtered colimits of compact Hausdorff spaces along injective transition maps. It is pretty clear that all CGWH spaces are of this form (being CG, it is the filtered colimit of the images of maps from CH spaces; and those images are themselves CH by WH); the other direction is e.g. Proposition A.14 in Schwede's "Global homotopy theory". | |
| Aug 9, 2022 at 8:57 | history | edited | Peter Kropholler | CC BY-SA 4.0 |
added 609 characters in body
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| Aug 8, 2022 at 12:01 | comment | added | Tyrone | Filtered colimits of compact Hausdorff spaces need not be weakly Hausdorff. See Ex. 2 on pg.422 of Dugundji's Topology book. Maybe you want to be clearer about which colimits you wish to allow and where they should be computed? | |
| Aug 6, 2022 at 6:46 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
a minor typo
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| Aug 6, 2022 at 6:42 | history | asked | Peter Kropholler | CC BY-SA 4.0 |