Timeline for Does homeomorphic and isomorphic always imply homeomorphically isomorphic?
Current License: CC BY-SA 2.5
17 events
| when toggle format | what | by | license | comment | |
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| Feb 22, 2013 at 5:43 | answer | added | Tom Goodwillie | timeline score: 17 | |
| Feb 21, 2013 at 16:55 | comment | added | YCor | Anyway "homeomorphically isomorphic" is pretty clear and not ambiguous. Sometimes it's better to use a clear wording than the usual one. Here I wouldn't say that "isomorphic as topological groups" is bad. Also to view a topological group as a triple (set, group law, topology) is just a point of view and I wouldn't call it pedantic. (wow I just realize that the thread is 3 years old... still I post the comment) | |
| Feb 21, 2013 at 16:11 | comment | added | S. Carnahan♦ | @Jason: The Lie group version was asked at mathoverflow.net/questions/114595/… | |
| Feb 21, 2013 at 4:38 | answer | added | Włodzimierz Holsztyński | timeline score: 9 | |
| Jan 4, 2011 at 20:07 | answer | added | Steven Gubkin | timeline score: 59 | |
| Oct 30, 2010 at 5:46 | answer | added | Ady | timeline score: 18 | |
| Oct 29, 2010 at 15:03 | comment | added | Jason DeVito - on hiatus | Does anyone know what happens if we require G and H to be Lie groups? | |
| Oct 29, 2010 at 9:53 | answer | added | Jonathan Kiehlmann | timeline score: 15 | |
| Oct 29, 2010 at 6:55 | vote | accept | CommunityBot | ||
| Oct 29, 2010 at 6:51 | comment | added | Martin Brandenburg | @KConrad: Rather "group isomorphic + homeomorphic => topological group isomorphic" because we are talking about objects and not about morphisms. | |
| Oct 29, 2010 at 6:40 | answer | added | Greg Kuperberg | timeline score: 116 | |
| Oct 29, 2010 at 6:33 | comment | added | KConrad | As for different wording in the title: "Does group isom. and homeomorphism imply topological group isom.?" | |
| Oct 29, 2010 at 6:33 | comment | added | KConrad | I didn't mean only the phrase "homeomorphically isomorphic" is awkward, but the way of talking about topological groups as ordered triples is awkward. What you wrote is logically correct, but is too pedantic. Rudin has a comment along these lines about writing measure spaces as ordered triples (4-tuples?) in the first chapter of his Real and Complex Analysis. Admittedly your question is precisely about this kind of pedanticness, but it's still better here to use words and talk about the sense in which objects are isomorphic ("as topological spaces", etc.). | |
| Oct 29, 2010 at 6:13 | comment | added | user5810 | I changed the phrasing in the body, although I think that would be too long for the title. | |
| Oct 29, 2010 at 6:10 | history | edited | user5810 | CC BY-SA 2.5 |
changed phrasing
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| Oct 29, 2010 at 6:00 | comment | added | KConrad | Like your previous question mathoverflow.net/questions/43937/… this is very awkwardly written. Nobody says "homeomorphically isomorphic", but rather "isomorphic as topological groups". A better way of expressing yourself would be: "Is there an example of non-isomorphic topological groups which are isomorphic as topological spaces and isomorphic as groups?" | |
| Oct 29, 2010 at 5:20 | history | asked | user5810 | CC BY-SA 2.5 |