Timeline for Сomplete homogeneous space which is not locally compact
Current License: CC BY-SA 2.5
10 events
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| Aug 3, 2010 at 15:59 | comment | added | Victor Protsak | Any topological vector space $V$ is homogeneous viewing addition as an action of the underlying group of $V$ on $V.$ | |
| Aug 3, 2010 at 15:17 | vote | accept | Ivan Gundyrev | ||
| Aug 3, 2010 at 14:22 | comment | added | Anweshi | I have edited the answer. | |
| Aug 3, 2010 at 14:21 | history | edited | Anweshi | CC BY-SA 2.5 |
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| Aug 3, 2010 at 14:08 | comment | added | Anweshi | @Ivan: In any case, Sergei Ivanov assures us that Banach spaces are homogeneous. Infinite dimensional Banach spaces are complete and not locally compact. Therefore it would be an example. If you want a concrete example you can take the space of continuous functions on an interval, with supremum norm. | |
| Aug 3, 2010 at 14:05 | comment | added | Ivan Gundyrev | I mean Definition: A metric space $(X,d)$ is called homogeneous if the group of its isometries acts transitively on $(X,d)$. | |
| Aug 3, 2010 at 14:03 | comment | added | Anweshi | @Sergei Ivanov: The wikipedia article gives the definition only for vector spaces. I have edited the answer to include this. | |
| Aug 3, 2010 at 14:02 | history | edited | Anweshi | CC BY-SA 2.5 |
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| Aug 3, 2010 at 14:01 | comment | added | Sergei Ivanov | What is $\alpha x$ for a metric space? I think that "homogeneous" means that the isometry group is transitive. Anyway, Banach spaces are homogeneous. | |
| Aug 3, 2010 at 13:56 | history | answered | Anweshi | CC BY-SA 2.5 |