Timeline for Meager subgroups of compact groups
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 27, 2015 at 9:18 | vote | accept | tomasz | ||
| Aug 27, 2015 at 9:17 | comment | added | tomasz | Right, of course. Well, you might as well take a quotient by ${\bf Z}$. I thought about that, but then took a glance at the paper and was mildly distressed with the use of convex hulls at the very beginning -- they would have been useless in the circle group. But of course this is locally just taking a countable union, so it preserves both borelness and meagreness of the subgroup, and if we had a "bad" (actually good) cover of the quotient, we could just pull it back to the reals, since meagreness is a local property. So thanks again. :) | |
| Aug 26, 2015 at 21:36 | comment | added | Taras Banakh | To obtain a "compact" example, take the quotient of the real line by the cyclic subgroup $C$ generated by a point n the Borel subgroup $H$ constructed by Laczkovich. Then $H/C$ with a Borel subgrop of the compact group $R/C$ which does not admit the desired representation. | |
| Aug 26, 2015 at 12:21 | comment | added | tomasz | Actually, I withdraw my comment: the group of reals is not compact, just locally compact, so it does not really answer my question. Can this be easily fixed? | |
| Aug 26, 2015 at 2:15 | comment | added | tomasz | Thanks, this answers my question completely. :) (If not in the direction I had hoped for.) | |
| Aug 26, 2015 at 2:14 | vote | accept | tomasz | ||
| Aug 26, 2015 at 12:19 | |||||
| Aug 25, 2015 at 18:31 | history | edited | Taras Banakh | CC BY-SA 3.0 |
More explanations of Laczkovich results
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| Aug 24, 2015 at 21:16 | history | answered | Taras Banakh | CC BY-SA 3.0 |