Timeline for Do closed hypersurfaces separate the euclidean space?
Current License: CC BY-SA 4.0
7 events
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| Apr 30, 2019 at 2:25 | comment | added | Ryan Budney | In the case of the point-set topology "closed" then the answer is yes, those do separate. The proof is basically the same as when dealing with compact manifolds. | |
| Apr 30, 2019 at 1:35 | review | Close votes | |||
| Apr 30, 2019 at 20:44 | |||||
| Apr 30, 2019 at 0:26 | comment | added | RBega2 | @AlexandreEremenko It's possible that the that this is asking for the hypersurface to be proper (i.e. so it is closed as a subset). | |
| Apr 29, 2019 at 21:13 | comment | added | Ryan Budney | Usually "closed" in this context means compact and without boundary. Your question appears to be about the case where you drop compactness, i.e. your manifold simply has no boundary, like $\mathbb R^{N-1}$. In that case the answer is no, as Euclidean spaces are diffeomorphic to open balls. | |
| Apr 29, 2019 at 21:01 | comment | added | Alexandre Eremenko | You have to define more precisely that is a "closed connected hypersurface" to make this meaningful. | |
| Apr 29, 2019 at 19:13 | history | edited | Michael Albanese | CC BY-SA 4.0 |
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| Apr 29, 2019 at 18:08 | history | asked | Antonio J. Urena | CC BY-SA 4.0 |