Timeline for Finite sets are residual in the Hausdorff space
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 18, 2022 at 3:37 | comment | added | Taras Banakh | The hyperspace of finite subset is dense in the hyperspace of compact subsets but not in the hyperspace of all closed sets (because the latter is not separable for non-compact $X$). | |
| Jun 14, 2022 at 8:01 | comment | added | ABIM | @YCor I also modified the post to further ask, if there is a "typical/standard" topology on $\mathbb{H}(X)$ for which the collection of finite sets is residual? | |
| Jun 14, 2022 at 8:00 | history | edited | ABIM | CC BY-SA 4.0 |
added 93 characters in body
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| Jun 14, 2022 at 7:51 | history | edited | ABIM | CC BY-SA 4.0 |
deleted 1 character in body
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| Jun 13, 2022 at 22:44 | comment | added | YCor | The set of nonempty finite subsets of cardinal $\le n$ is closed. Moreover, if $X$ has no isolated point, then it has empty interior. Hence if $X$ has no isolated point, the set of nonempty finite subsets is an $F_\sigma$ of empty interior (i.e., the complement of a $G_\delta$-dense subset, i.e., of a residual subset). So it's not residual (for $X$ nonempty with no isolated point). | |
| S Jun 13, 2022 at 21:40 | history | suggested | Yankl | CC BY-SA 4.0 |
Fixed typo
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| Jun 13, 2022 at 19:25 | review | Suggested edits | |||
| S Jun 13, 2022 at 21:40 | |||||
| Jun 13, 2022 at 18:51 | history | asked | ABIM | CC BY-SA 4.0 |