Timeline for Does geometric realization commute with passing to the compactly generated topology?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 11, 2018 at 3:15 | comment | added | Dan Ramras | For what it's worth, I now think a better question is whether the maps in my question are weak homotopy equivalences, rather than homeomorphisms. | |
| Jun 8, 2018 at 2:41 | comment | added | Dan Ramras | @TarasBanakh I suspect the following is true, but haven't checked carefully: if the spaces $X_n$ are all Hausdorff, then the equivalence relation that defines the "thick" geometric realization is closed. Thus a positive answer to the my "general question" for closed equivalence relations ought to give a positive answer to the main question if one uses thick realization and assumes the spaces are Hausdorff. I'd be happy if that could be proven. | |
| Jun 6, 2018 at 11:20 | comment | added | Taras Banakh | @DanRamras Should the equivalence relation $\sim$ be closed in $X\times X$ or not? | |
| Jun 2, 2018 at 20:42 | comment | added | Dan Ramras | @DenisNardin My guess is that the second question is false in general, and I can imagine that your formulation might be the best way to look for a counterexample. | |
| Jun 2, 2018 at 19:44 | comment | added | Denis Nardin | Your second question can be rephrased as asking whether the topology of kR is a subspace of k(X×X), where R < X×X is the equivalence relation with the subspace topology. I don't know if it makes it easier or harder... | |
| Jun 2, 2018 at 18:43 | history | asked | Dan Ramras | CC BY-SA 4.0 |