Timeline for Is there a natural topology for subsets of a fixed topological space?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| 2 hours ago | comment | added | Emily | I also recommend this book and this paper, both of which talk about the Vietoris topology, one of the more common topologies on sets of subsets, on all of $\mathcal{P}(X)$, rather than only on the set $\mathrm{Cld}(X)$ of closed subspaces of $X$. | |
| 2 hours ago | comment | added | Emily | I'm currently writing a chapter on exactly this, but it will take a long while until everything is done. Here's a preliminary version. | |
| 7 hours ago | comment | added | user39598 | @PietroMajer Indeed one could do that but since there aren't that many topologies on 2, this would basically be saying that an open subset of $P(X)$ consists of subsets of X that agree on various compacts. This seems quite restrictive and doesn't really generalize the Hausdorff distance. | |
| 8 hours ago | comment | added | Pietro Majer | You could identify every subset of $X$ with its characteristic function $X\to \mathbb 2$, and put on $P(X)$ the compact open topology of this set of mappings. | |
| 9 hours ago | comment | added | Steven Clontz | en.m.wikipedia.org/wiki/Hypertopology | |
| 9 hours ago | history | asked | user39598 | CC BY-SA 4.0 |