Timeline for Does there exist any subspace of R^n, homeomorhic to a manifold but not a C^0 submanifold of R^n?
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| Apr 9, 2014 at 20:37 | review | Close votes | |||
| Apr 10, 2014 at 17:45 | |||||
| Apr 5, 2014 at 14:57 | comment | added | Paladin | wiki "local flatness" | |
| Apr 5, 2014 at 14:01 | comment | added | Alexandre Eremenko | Could you include a definition of a $C^0$ submanifold? | |
| Apr 4, 2014 at 21:02 | comment | added | Piotr Pstrągowski | In fact someone already gave this example and, as I understand it, answered this question here mathoverflow.net/questions/79431/locally-flat-submanifold?rq=1 | |
| Apr 4, 2014 at 20:47 | comment | added | Piotr Pstrągowski | I imagine that the counterexamples to Schoenflies problem, ie. the wild spheres $S^2 \subseteq \mathbb{R}^3$ could give what you're looking for. If such a wild sphere was a submanifold, it would be locally flat and by a theorem of Morton Brown (see en.wikipedia.org/wiki/Schoenflies_problem) thus not wild at all, giving a contradiction. | |
| Apr 4, 2014 at 20:39 | history | edited | user9072 |
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| Apr 4, 2014 at 20:23 | review | First posts | |||
| Apr 4, 2014 at 20:33 | |||||
| Apr 4, 2014 at 20:16 | history | edited | Paladin |
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| Apr 4, 2014 at 20:09 | history | edited | Ben McKay | CC BY-SA 3.0 |
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| Apr 4, 2014 at 20:04 | history | asked | Paladin | CC BY-SA 3.0 |