Timeline for Question about product topology
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 4, 2013 at 6:52 | vote | accept | duodaa | ||
| Jun 27, 2013 at 18:23 | answer | added | Ashutosh | timeline score: 5 | |
| Jun 26, 2013 at 13:49 | history | edited | duodaa | CC BY-SA 3.0 |
edited body
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| Jun 26, 2013 at 12:15 | comment | added | Włodzimierz Holsztyński | I wonder if this question is related to the continuum hypothesis. What about sets $S$ which have an intermediate cardinality? | |
| Jun 26, 2013 at 11:21 | comment | added | Misha | Also, for every $G_{\delta}$-subset $S$ of ${\mathbb R}$ which is dense and has empty interior, one has $S\cong S\times S$. The reason is that such $S$ is a Polish space and, hence, Alexandrov-Uryson theorem implies that both $S$ and $S\times S$ are homeomorphic to ${\mathbb R}\setminus {\mathbb Q}$. | |
| Jun 26, 2013 at 11:08 | comment | added | Misha | The question seems to be well within the scope of MO, compare mathoverflow.net/questions/26001/… with an answer containing a reference to several proofs of Sierpinsky's theorem, that provides a partial answer to the OP question. | |
| Jun 26, 2013 at 9:46 | comment | added | Włodzimierz Holsztyński | @user35739: I would first of all wonder about a full characterization of the spaces $S$ with the property of having all (relative) open intervals homeomorphic one to another. There is no need a priori to mention anything about $S$ being dense or having empty interior (it's that elegant :-). | |
| Jun 26, 2013 at 9:41 | comment | added | Włodzimierz Holsztyński | @Andras: would you explain why? | |
| Jun 26, 2013 at 8:07 | review | Close votes | |||
| Jun 26, 2013 at 16:22 | |||||
| Jun 26, 2013 at 7:57 | review | First posts | |||
| Jun 26, 2013 at 9:59 | |||||
| Jun 26, 2013 at 7:53 | history | edited | duodaa | CC BY-SA 3.0 |
added 29 characters in body
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| Jun 26, 2013 at 7:48 | comment | added | András Bátkai | Dear @user35739, your question is probably better suited at math.stackexchange.com, see the FAQ of this site. | |
| Jun 26, 2013 at 7:39 | history | asked | duodaa | CC BY-SA 3.0 |