Timeline for When (why) did we allow manifolds to be non-Hausdorff and/or non-second countable?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 4, 2020 at 9:59 | comment | added | Praphulla Koushik | Oh.. I will check that :) | |
| Jun 4, 2020 at 9:00 | comment | added | Dmitri Pavlov | @PraphullaKoushik: Moerdijk and Mrčun: Introduction to foliations and Lie groupoids. | |
| Jun 4, 2020 at 8:26 | comment | added | Praphulla Koushik | :) I understand what you mean.. Yes, Yes, sheaves of sets on a site.. can you suggest me to look at some paper which (one of which) started using this possibility of non-Hausdorff non-paracompact manifolds.. | |
| Jun 4, 2020 at 7:31 | comment | added | Dmitri Pavlov | @PraphullaKoushik: No, and you cannot make such inferences from such a use of language. Just like when somebody says “nonunital ring”, it does not mean that rings are not assumed to be unital. See ncatlab.org/nlab/show/red+herring+principle. | |
| Jun 4, 2020 at 7:29 | comment | added | Dmitri Pavlov | @PraphullaKoushik: The étale space construction works for sheaves of sets on any site. In particular, for sheaves of sets on manifolds it produces a (typically) non-Hausdorff non-paracompact manifold. | |
| Jun 4, 2020 at 7:15 | comment | added | Praphulla Koushik | "non-Hausdorff and nonparacompact spaces (e.g., smooth manifolds)" so, for you smooth manifolds are not necessarily Hausdorff and paracompact?? | |
| Jun 4, 2020 at 7:14 | comment | added | Praphulla Koushik | By etale space construction do you mean the one from sheaves on a topological space $X$? This is the only etale space construction I know. | |
| Jun 4, 2020 at 7:03 | history | answered | Dmitri Pavlov | CC BY-SA 4.0 |