Timeline for What can say about $2^X= \{A\subseteq X: A\text{ is closed set} \}$, when $(X, \mathcal{U})$ is a compact uniform space?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 31, 2018 at 18:41 | history | edited | Michael Hardy | CC BY-SA 4.0 |
deleted 2 characters in body; edited title
|
| Dec 31, 2018 at 8:04 | comment | added | Wlod AA | Every Hausdorff compact space $X$ has EXACTLY one uniformity (basically, given by the neighborhoods of the diagonal of space $X^2$ in $X^2$. This induces a compact topology (and uniformity) in $2^X$. This generalizes the Hausdorff metric in the metric case. | |
| Dec 30, 2018 at 22:10 | answer | added | KP Hart | timeline score: 4 | |
| Dec 26, 2018 at 22:53 | comment | added | Henno Brandsma | In the original paper(s) by E. Michael where he introduced the Vietoris topology, he also discusses the uniformity in $2^X$. I'd start there. | |
| Dec 24, 2018 at 18:26 | comment | added | Forever Mozart | Well, it is compact Hausdorff (in the Vietoris topology). But I suppose you're asking what uniformity adds to the picture. | |
| Dec 24, 2018 at 14:55 | review | First posts | |||
| Dec 24, 2018 at 15:15 | |||||
| Dec 24, 2018 at 14:53 | history | asked | user479859 | CC BY-SA 4.0 |