Timeline for Is it true that $X\times I\sim Y\times I\implies X\sim Y$?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Nov 30, 2017 at 19:53 | comment | added | Andres Mejia | This showed up in the Saint Petersburg Topology olympiad, I wonder if this was the reference mathcenter.spb.ru/nikaan/olympiad/problemseng.pdf | |
| Jan 31, 2017 at 20:19 | comment | added | Włodzimierz Holsztyński | Let me at least provide the first step (the easiest one but crucial): consider spaces $\ X'\ $ and $\ Y'\ $ obtained from $\ X\times[0;\infty)\ $ and $\ Y\times[0;\infty)\ $ respectively, by removing from them the points which are the centers of 3-dim balls contained in those Cartesian products. | |
| Jan 31, 2017 at 20:13 | comment | added | Włodzimierz Holsztyński | @Joël, actually, spaces $\ X\times[0;\infty]\ $ and $\ Y\times[0;\infty]\ $ are not homeomorphic. I am confident that I've proved it--for Wlodek K's example as well as for mine, for both. It'd be awkward to present my proof in a comment (while the thread seems to be closed, and further answer are not allowed). | |
| Jan 31, 2017 at 16:22 | comment | added | Joël | Oh yes, I see where I was wrong. In fact I don't know if $X \times I$ and $Y \times I$ are homeomorphic if $I$ is a half-line. | |
| Jan 31, 2017 at 16:20 | comment | added | Joël | Really? Then my intuition must be wrong. I'll think more. | |
| Jan 31, 2017 at 8:33 | vote | accept | timon92 | ||
| Jan 31, 2017 at 6:57 | comment | added | Włodzimierz Holsztyński | @Joël, I fully agree with your first sentence while I have doubts about your second sentence of your comment. | |
| Jan 31, 2017 at 3:30 | comment | added | Joël | Nice example and picture. And that works as well with $I$ replaced by the half-line. | |
| Jan 30, 2017 at 23:55 | history | edited | Wlodek Kuperberg | CC BY-SA 3.0 |
rephrasing the whole answer.
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| Jan 30, 2017 at 23:46 | history | undeleted | Wlodek Kuperberg | ||
| Jan 30, 2017 at 23:30 | history | deleted | Wlodek Kuperberg | via Vote | |
| Jan 30, 2017 at 23:28 | history | answered | Wlodek Kuperberg | CC BY-SA 3.0 |