Timeline for Polish groups with no small subgroups
Current License: CC BY-SA 4.0
10 events
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| Jun 15, 2019 at 20:26 | comment | added | YCor | But obviously an infinite product of discrete groups is pro-discrete and has small subgroups (and is not locally compact unless all but finitely many are finite). | |
| Jun 15, 2019 at 14:36 | comment | added | Jackson Morrow | @YCor My apologies! There was a missing "every" in the question. I have corrected the statement. Thanks again! | |
| Jun 15, 2019 at 14:35 | history | edited | Jackson Morrow | CC BY-SA 4.0 |
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| Jun 14, 2019 at 21:51 | comment | added | YCor | I don't understand the wording in Q3. Is "every" or "some" or "no" missing? | |
| Jun 14, 2019 at 21:42 | history | edited | Jackson Morrow | CC BY-SA 4.0 |
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| Jun 14, 2019 at 21:23 | comment | added | Jackson Morrow | @YCor thank you for your comments! The phrasing of Q2 was not very precise, but yes I was asking for generalizations of the results of Gleason, Montgomery-Zippin and Yamabe. I have edited the question a bit since I am interested in a certain type of Polish group having no small subgroups. | |
| Jun 13, 2019 at 21:13 | comment | added | YCor | Q2: one short answer is "yes, there are." If more precisely you're asking whether there are generalizations of this result of Gleason, Montgomery-Zippin and Yamabe, to a broader setting, I don't know. One can ask whether for Polish groups, "no small subgroups" implies "locally contractible". I'd guess counterexamples are known, but this is speculation. | |
| Jun 13, 2019 at 21:08 | comment | added | YCor | Q1: any infinite-dimensional Banach space makes the job. | |
| Jun 13, 2019 at 21:07 | history | edited | YCor | CC BY-SA 4.0 |
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| Jun 13, 2019 at 19:30 | history | asked | Jackson Morrow | CC BY-SA 4.0 |