Timeline for Is an open subset of a cofibration a cofibration?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 14, 2021 at 21:00 | answer | added | John Rognes | timeline score: 2 | |
| Feb 13, 2021 at 0:51 | answer | added | skupers | timeline score: 5 | |
| Feb 12, 2021 at 18:16 | comment | added | user1092847 | @Tim Thanks, I would be interested in knowing the answer for both Serre and Hurewicz cofibrations, especially if the answer is negative for one and positive for the other. Perhaps more broadly my question is: what is the largest class of topological spaces and cofibrations for which this property holds? | |
| Feb 12, 2021 at 18:06 | comment | added | Tim Campion | Probably, whichever category you use, Hurewicz cofibrations (as opposed to Serre cofibrations) are closed under pullback along open embeddings, but not under pullback along all maps. Note that in the universal diagram May uses, there's a mapping cylinder. Mapping cylinders involve both a product and a pushout to construct. Pushouts do not necessarily commute with pullbacks in any category of topological spaces. OTOH, pushouts do commute with pullbacks in simplicial sets. Indeed, cofibrations of simplicial sets are just monomorphisms, which are closed under pullback along an arbitrary map. | |
| Feb 12, 2021 at 18:01 | comment | added | Tim Campion | Since you refer to May's Concise Course, I infer that "topological space" means compactly-generated weak-Hausdorff space, right? And "cofibration" means CGWH-Hurewicz cofibration? | |
| Feb 12, 2021 at 17:58 | history | asked | user1092847 | CC BY-SA 4.0 |