Timeline for Does a coarser topology lead to a non-Hausdorff topological manifold? [closed]
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Feb 16 at 23:46 | history | closed |
Igor Belegradek Ryan Budney Moishe Kohan Daniele Tampieri Andy Putman |
Needs details or clarity | |
| Feb 16 at 22:38 | history | edited | Bastam Tajik | CC BY-SA 4.0 |
deleted 704 characters in body
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| Feb 16 at 9:55 | vote | accept | Bastam Tajik | ||
| Feb 16 at 6:53 | answer | added | Willie Wong | timeline score: 6 | |
| Feb 16 at 5:32 | comment | added | David Roberts♦ | @BastamTajik this is a reasonable move. I suggest asking in the special case that I outlined. And if it's not possible for balls in general, then there is nothing special to dimensions 4 and 2, and no amount of physical motivation will help. | |
| Feb 16 at 5:13 | comment | added | Bastam Tajik | @DavidRoberts maybe I can pose a question separately to see if the finer topology of my specific physical case, does result in a non-Hausdorff manifold (preferably of dimension 2) | |
| Feb 16 at 5:09 | comment | added | David Roberts♦ | @MoisheKohan I was hoping that there was good reason to suspect that such examples even exist, separately from the actual question in the post about non-smooth endofunctions. If we can rule out the case of a union of balls in Euclidean space, then I don't believe a more complicated example exists. The linked example doesn't help me. | |
| Feb 16 at 4:55 | comment | added | Moishe Kohan | I see no reason to expect existence of examples (of such change from Hausdorff to non-Hausdorff manifolds) of any kind. | |
| Feb 16 at 4:45 | comment | added | Bastam Tajik | dimension change from 4 to 2 is acceptable to me based on physical reasons. Please pay attention to the example here: mathoverflow.net/q/454368/503363 @MoisheKohan | |
| Feb 16 at 4:15 | comment | added | Moishe Kohan | @DavidRoberts: such examples do not exist if one wants to preserve the dimension. I doubt it will work if dimension changes either. | |
| Feb 16 at 2:22 | comment | added | David Roberts♦ | Do you have an example of such a non-Hausdorff, locally Euclidean topology on any smooth manifold? I suspect that wlog one could take such a thing and restrict to two charts in the coarse topology containing the non-separable points, and hence get an example that is the union of two balls in Euclidean space, analogous to the line with two origins. | |
| Feb 15 at 23:11 | comment | added | Bastam Tajik | @IgorBelegradek $f$ is clearly a diffeomorphism and one wants to know if the map remains smooth after changing the topology. | |
| Feb 15 at 23:06 | comment | added | Bastam Tajik | You absolutely have not understood the question @IgorBelegradek BTW I gave you the relevant links, but it seems you rather have no interest in reading the question carefully, otherwise you would understand that the Euclidean non-Hausdorff coarser exists by assumption. Once more I give an example, though I barely guess you take the responsibility of your closour vote! mathoverflow.net/q/454368/503363 | |
| Feb 15 at 23:02 | review | Close votes | |||
| Feb 16 at 23:52 | |||||
| Feb 15 at 22:52 | comment | added | Igor Belegradek | You simply re-posted the recently closed question without any expository improvements. It is unclear why coarsening the topology on a manifold can ever lead to a non-Hausdorff locally Euclidean space. It is unclear what is meant by "possesses singularities". I gather that your $f$ is meant to be a homeomorphism from a Hausdorff manifold to a non-Hausdorff one. Being Hausdorff is preserved under homeomorphisms so no such $f$ exists. | |
| Feb 15 at 21:31 | history | asked | Bastam Tajik | CC BY-SA 4.0 |