Timeline for When are all continuous self-maps of a topological spaces generated by retractions and self-homeomorphisms of prime order?
Current License: CC BY-SA 3.0
15 events
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| Sep 14, 2013 at 11:41 | vote | accept | Niemi | ||
| Sep 14, 2013 at 11:41 | vote | accept | Niemi | ||
| Sep 14, 2013 at 11:41 | |||||
| Sep 12, 2013 at 9:44 | answer | added | Niemi | timeline score: 4 | |
| Sep 12, 2013 at 9:41 | history | edited | Niemi | CC BY-SA 3.0 |
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| Sep 9, 2013 at 8:48 | history | edited | Niemi | CC BY-SA 3.0 |
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| Sep 6, 2013 at 19:28 | comment | added | Benjamin Steinberg | A more reasonable (but still virtually impossible) question would be for which spaces is every maps which is not a self-homeomorphism generated by retractions. Probably one also wants to put some conditions on the topology so that every bijective cts self-map is a homeomorphism. | |
| Sep 6, 2013 at 15:49 | history | edited | Niemi | CC BY-SA 3.0 |
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| Sep 6, 2013 at 15:42 | comment | added | Niemi | Fair enough, my motivation is as follows: Take the lattice of all submonoids of the monoid given by all continuous self-maps of a topological space. If am not mistaken, then the atoms in this lattice are precisely the monads generated by one of the (nontrivial) functions that I have listet in my question. Thus, I was interested whether the (lattice-)join of all these gives me the full monoid. | |
| S Sep 6, 2013 at 15:39 | history | suggested | James Cranch | CC BY-SA 3.0 |
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| Sep 6, 2013 at 15:35 | review | Suggested edits | |||
| S Sep 6, 2013 at 15:39 | |||||
| Sep 6, 2013 at 15:32 | comment | added | Todd Trimble | Where does this problem come from? Given the incomprehensible variety of topological space structures, I'd be inclined to suspect that a characterization over all topological spaces would be hopelessly difficult. | |
| Sep 6, 2013 at 15:26 | answer | added | Benjamin Steinberg | timeline score: 6 | |
| Sep 6, 2013 at 15:12 | history | edited | Niemi | CC BY-SA 3.0 |
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| Sep 6, 2013 at 15:00 | answer | added | James Cranch | timeline score: 4 | |
| Sep 6, 2013 at 14:53 | history | asked | Niemi | CC BY-SA 3.0 |