Timeline for Neighborhood basis of the identity in a locally profinite group
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 28, 2012 at 6:18 | vote | accept | Niccolo' | ||
| May 26, 2012 at 16:47 | answer | added | Igor Rivin | timeline score: 0 | |
| May 26, 2012 at 13:54 | comment | added | YCor | Number of mathscinet/google references: "locally profinite group": 11/4220 "totally disconnected locally compact group": 60/22700; "locally compact totally disconnected group" 23/16300. Wikipedia contains some nontrivial general nontrivial facts (Willis' theory) about totally disconnected LC-groups, inside the page "totally disconnected groups", but also redirects to a page "locally profinite groups" which essentially contains nothing. I hope the latter page will be renamed but I'm not technically qualified to do this. | |
| May 26, 2012 at 13:38 | comment | added | YCor | the terminology "locally profinite" is in contradiction with the mainstream use of "locally" in topological group theory. Its natural meaning would be: every compact subset is contained in a compact open subgroup. Many people deal with totally disconnected LC-groups (LC= locally compact) and they're only referred as "locally profinite" by a few people, mainly around Langlands's theory. | |
| May 26, 2012 at 9:58 | comment | added | vytas | it seems to me that a product over an uncountable set, something like $\prod_{x\in \mathbb R} \mathbb F_p$ will not have a countable basis. | |
| May 26, 2012 at 9:42 | comment | added | Julien Melleray | First, since you're only speaking of neighborhoods of identity, you may as well assume G=K is compact. Anyway, a Hausdorff topological group is metrizable if and only if it has a countable basis of neighborhoods of the identity (that is the Birkhoff-Kakutani theorem)- so the criterion you're looking for is simply the metrisability of the group. | |
| May 26, 2012 at 8:47 | history | asked | Niccolo' | CC BY-SA 3.0 |