Timeline for Is a separable compact Hausdorff space already metrizable?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 17, 2018 at 18:49 | comment | added | Roman Hric | Of course, it was clear after opening your link to counterexamples. Anyway, even the question might be dumb, the answers might be useful also to someone else. | |
| Aug 17, 2018 at 18:42 | comment | added | Alex M. | Since second-countability is equivalent to metrizability, and since there are separable compact Hausdorff spaces that are not metrizable (see my couterexamples link), it follows that separability is weaker than second-countability. | |
| Aug 17, 2018 at 18:37 | comment | added | Roman Hric | I should have formulated my question as follows: Is separability equivalent to 2nd countability in compact Hausdorff spaces? Sure I did the web search but didn't succeed to find the counterexamples. | |
| Aug 17, 2018 at 17:19 | comment | added | Alex M. | See also math.stackexchange.com/q/83652, math.stackexchange.com/q/1642751, math.stackexchange.com/q/573805, math.stackexchange.com/q/234018. Even more counterexamples here: math.stackexchange.com/q/74923. A web search (like I did) would have made posting your question needless. | |
| Aug 17, 2018 at 17:08 | history | answered | Alex M. | CC BY-SA 4.0 |