Timeline for Compactness and Covering Spaces
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 16, 2010 at 17:35 | comment | added | Anirbit | Ah..yes. I was mistaken to think that taking intersection on only 1 sheet should be enough. To define the kind of $U$ that Greg wanted one needs to take intersection on all the sheets and that will mess up. | |
| Jul 16, 2010 at 15:20 | comment | added | Willie Wong | @Anirbit: infinite intersections of open sets are not open. Because in the end you want a finite subcover from $\mathcal{C}$, so on each "sheet" you need to pick an open set in $\mathcal{C}$ containing $U$. | |
| Jul 16, 2010 at 9:57 | comment | added | Anirbit | Can you enlighten as to what is the closest statement that may be true for infinite sheeted covers? I understand that for a cover downstairs to lift to a cover upstairs one needs the number of sheets to be finite but why does the definition of $U$ depend on finiteness of the number of sheets? Take a locally trivializing neighbourhood of $p$ and look at some intersection of its pre-image with some open set in $C$ and then project it down. Doesn't that give the kind of $U$ one needs? May be I am missing something obvious! | |
| Jul 16, 2010 at 5:13 | history | answered | Greg Kuperberg | CC BY-SA 2.5 |