Timeline for Families that can arise as compacts wrt a topology
Current License: CC BY-SA 4.0
7 events
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| Dec 23, 2019 at 22:06 | comment | added | Henno Brandsma | There is the class of anti-compact spaces $X$ where a subspace of $X$ is compact iff the subspace is finite (i.e. when it is forced to be, by cardinality). Discrete spaces are an example, and the cocountable topology on an uncountable set. It only shows that the finite sets are realisable in quite different ways.. | |
| Dec 21, 2019 at 17:56 | comment | added | Gro-Tsen |
Here's the question about algebras for the ultrafilter monad (to create a link, write [text](URL of link)).
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| Dec 21, 2019 at 12:03 | comment | added | Andrea Marino | It would be a starting point, but my initial motivation deals with the family of compact, non necessarily hausdorff, subsets! I don't know how to link, I am referring to "what are the algebras for the ultrafilter monad on topological spaces"? | |
| Dec 21, 2019 at 11:58 | comment | added | Gro-Tsen | Maybe it would be simpler to ask the question for compact Hausdorff subsets of $X$ (not assuming $(X,T)$ itself Hausdorff, or even [quasi-]compact)? Compact Hausdorff often behaves better than quasi-compact, and specifically, in this case, they are automatically closed. So, a variant of your question: can we characterize families $\mathscr{K}\subseteq\mathscr{P}(X)$ which are the compact Hausdorff subspaces of $X$ for some topology on $X$ (with no assumptions on this topology)? | |
| Dec 21, 2019 at 11:42 | history | edited | Andrea Marino | CC BY-SA 4.0 |
added 12 characters in body
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| Dec 21, 2019 at 2:47 | history | edited | Andrea Marino | CC BY-SA 4.0 |
added 192 characters in body
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| Dec 21, 2019 at 2:16 | history | asked | Andrea Marino | CC BY-SA 4.0 |