Timeline for Two vector spaces with homeomorphic open subsets are isomorphic?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Sep 30, 2015 at 10:19 | comment | added | shasta | Yes. The interesting question between those two extremes is the case of Lipschitz equivalence (for Banach spaces). Again much work has been done on this case, e.g. by Lindenstrauss et al. | |
| Sep 30, 2015 at 10:06 | comment | added | usr203050 | My guess for the second part is that the differential at some point (or may be at any point) can give an isomorphism between the two spaces. | |
| Sep 30, 2015 at 9:57 | vote | accept | usr203050 | ||
| Sep 30, 2015 at 9:54 | answer | added | shasta | timeline score: 11 | |
| Sep 30, 2015 at 9:51 | comment | added | usr203050 | My guess is that it is true in all spaces, since it is true for finite-dimentional ones. But I cannot give a proof or a disproof. | |
| Sep 30, 2015 at 9:49 | comment | added | Simon Rose | I would guess that the first question is false, simply on the grounds that it is pretty trivially true for finite dimensional ones, so it's probably false for arbitrary vector spaces. | |
| Sep 30, 2015 at 9:19 | history | asked | usr203050 | CC BY-SA 3.0 |