Timeline for Infinite topological spaces such that every subset is a retract
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 10, 2014 at 7:09 | vote | accept | Dominic van der Zypen | ||
| Dec 10, 2014 at 7:09 | vote | accept | Dominic van der Zypen | ||
| Dec 10, 2014 at 7:09 | |||||
| Dec 9, 2014 at 17:42 | answer | added | Eric Wofsey | timeline score: 8 | |
| Dec 9, 2014 at 17:38 | answer | added | François G. Dorais | timeline score: 3 | |
| Dec 9, 2014 at 16:54 | comment | added | Eric Wofsey | A disjoint union of a discrete and an indiscrete space is also an example. More generally, a space has this property iff its $T_0$ quotient does. | |
| Dec 9, 2014 at 16:51 | comment | added | François G. Dorais | @Emil: The two-element subspaces of a $T_1$ space are discrete, so such a space would be Hausdorff. But there are no non-discrete Hausdorff spaces where every subset is a retract: mathoverflow.net/a/189292 | |
| Dec 9, 2014 at 16:32 | comment | added | Emil Jeřábek | It can (see below). What I do not see is whether there can be $T_1$ counterexamples. | |
| Dec 9, 2014 at 16:28 | answer | added | Emil Jeřábek | timeline score: 6 | |
| Dec 9, 2014 at 16:15 | comment | added | Dominic van der Zypen | You're absolutely right -- I apologise. Now I'm looking for infinite counterexamples. Maybe your example can be adapted to infinity (I don't see how yet, though). | |
| Dec 9, 2014 at 16:14 | history | edited | Dominic van der Zypen | CC BY-SA 3.0 |
added 31 characters in body; edited title
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| Dec 9, 2014 at 16:14 | history | undeleted | Dominic van der Zypen | ||
| Dec 9, 2014 at 16:05 | history | deleted | Dominic van der Zypen | via Vote | |
| Dec 9, 2014 at 16:04 | comment | added | Emil Jeřábek | No, the Sierpiński space also has this property. | |
| Dec 9, 2014 at 15:59 | history | asked | Dominic van der Zypen | CC BY-SA 3.0 |