Timeline for $T_2$-spaces where all non-empty open sets are homeomorphic
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 16, 2018 at 22:24 | history | edited | N. de Rancourt | CC BY-SA 4.0 |
added 285 characters in body
|
| May 16, 2018 at 12:55 | comment | added | Will Brian | @N.deRancourt: Go ahead and add it to your answer -- it's just a minor variation on your idea. | |
| May 16, 2018 at 9:57 | comment | added | N. de Rancourt | Of course @WillBrian you are right! That's nice, maybe you should post it as an answer? Or if you prefer, I can add it on my answer. | |
| May 15, 2018 at 20:45 | comment | added | Dominic van der Zypen | @N.deRancourt I like your answer so much that I have accepted it! Answers from other people are of course much welcome, too. | |
| May 15, 2018 at 17:31 | vote | accept | Dominic van der Zypen | ||
| May 15, 2018 at 14:14 | comment | added | Will Brian | Doesn't your argument apply equally well to the subspace of $X^\omega$ consisting of eventually constant sequences? It's still true that the closed sets can be expressed as trees, and it's still true that every open set is a union of disjoint cones. But this subspace has cardinality $|X|$, so this version of the argument would work for any infinite cardinal. | |
| May 15, 2018 at 13:46 | comment | added | N. de Rancourt | However @DominicvanderZypen, maybe you should not accept the answer yet, the question is still interesting as we have no example for a lot of cardinals. It would be nice if other people could look at this question. | |
| May 15, 2018 at 13:44 | history | edited | N. de Rancourt | CC BY-SA 4.0 |
deleted 3 characters in body
|
| May 15, 2018 at 13:43 | comment | added | N. de Rancourt | Yes @NikWeaver, Will Brian was right: it was "empty interior". I edit to correct the mistake. | |
| May 15, 2018 at 13:40 | vote | accept | Dominic van der Zypen | ||
| May 15, 2018 at 14:33 | |||||
| May 15, 2018 at 13:01 | comment | added | Will Brian | @NikWeaver: I think it should say empty interior. | |
| May 15, 2018 at 12:59 | comment | added | Nik Weaver | Every nonempty compact subset of $\omega^\omega$ has nonempty interior? What about singletons? | |
| May 15, 2018 at 12:40 | history | answered | N. de Rancourt | CC BY-SA 4.0 |