Timeline for Can one characterize those sheaves which have Hausdorff etale spaces?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Feb 16, 2023 at 10:46 | answer | added | Elías Guisado Villalgordo | timeline score: 0 | |
| Oct 16, 2012 at 12:54 | answer | added | John Stalfos | timeline score: 1 | |
| Jul 19, 2012 at 19:11 | comment | added | David Carchedi | Another comment along these lines: $E(F)$ can only be Hausdorff if $X$ is locally Hausdorff. Also, if $X$ is locally Hausdorff, then one can choose a covering by Hausdorff neighborhoods, and the canonical projection to $X$ from the disjoint union of the elements of this cover is a local homeomorphism, hence a sheaf. This generalizes Mike's example. | |
| Jul 19, 2012 at 17:31 | comment | added | Mike Shulman | For what it's worth, in case anyone else is confused, here is an example of a well-supported sheaf on a non-Hausdorff space whose total space is Hausdorff. Let $X$ be the real line with a doubled origin, and let $E(F) = \mathbb{R} + \mathbb{R}$ with the two maps to $X$ being two "copies of the identity" one going through each copy of the origin. Then $E(F)$ is certainly Hausdorff and its map to $X$ is surjective, and it's easy to see that it is also a local homeomorphism. | |
| Jul 17, 2012 at 17:05 | answer | added | David Carchedi | timeline score: 0 | |
| Jul 17, 2012 at 13:57 | comment | added | David Carchedi | Changed accordingly. | |
| Jul 17, 2012 at 13:56 | history | edited | David Carchedi | CC BY-SA 3.0 |
edited title
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| Jul 17, 2012 at 12:12 | comment | added | Martin Brandenburg | I would like to suggest "Can one characterize Hausdorff étale spaces" as a title. | |
| Jul 17, 2012 at 10:42 | history | asked | David Carchedi | CC BY-SA 3.0 |