Timeline for Open subspaces of CW complexes
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 26, 2019 at 23:23 | history | became hot network question | |||
| Aug 26, 2019 at 20:18 | comment | added | John Rognes | One of Cauty's counterexamples has only three cells, so the problem is not about finiteness, but rather about the attaching maps. Regular CW complexes can be triangulated, and open subsets of simplicial complexes can again be triangulated, so it is true that open subsets of regular CW complexes are CW spaces. | |
| Aug 26, 2019 at 20:13 | vote | accept | Jeff Strom | ||
| Aug 26, 2019 at 20:12 | comment | added | Ryan Budney | As John mentions, there are counter-examples to open subsets of CW-complexes being CW-complexes, but I believe under reasonable "finiteness" assumptions the result should be true. I have not looked at the counter-examples John cites but I imagine they are due to the CW-complex having fairly "bad" attaching maps. In my mind I'm imagining an adaptation of the proof that open subsets of $\mathbb R^n$ admit CW-structures. | |
| Aug 26, 2019 at 19:47 | answer | added | John Rognes | timeline score: 19 | |
| Aug 26, 2019 at 15:11 | history | asked | Jeff Strom | CC BY-SA 4.0 |