Timeline for Meager subgroups of compact groups
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 27, 2015 at 9:18 | vote | accept | tomasz | ||
| Aug 26, 2015 at 16:07 | history | edited | Nate Eldredge | CC BY-SA 3.0 |
fix typo in title
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| Aug 26, 2015 at 12:45 | history | edited | tomasz | CC BY-SA 3.0 |
edited title
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| Aug 26, 2015 at 2:14 | vote | accept | tomasz | ||
| Aug 26, 2015 at 12:19 | |||||
| Aug 24, 2015 at 21:16 | answer | added | Taras Banakh | timeline score: 7 | |
| Aug 18, 2015 at 19:28 | comment | added | Boaz Tsaban | @AlexRavsky: Could you update on your progress with this problem? | |
| Aug 18, 2015 at 13:08 | comment | added | tomasz | @BoazTsaban: I don't assume that, but an answer under that assumption (even one which just said that so-and-so is consistent) would still be nice. It's been some time since I was considering that, but if I recall correctly, I hadn't seen any reason for that to be a WLOG kind of assumption. And again, you might also assume that the $H_n$ are analytic in a suitable sense, if that helps obtain a positive answer. | |
| Aug 17, 2015 at 21:40 | comment | added | Boaz Tsaban | Tomasz, could you state clearly in the problem whether you assume that the sets $H_n$ are symmetric? May this be assumed WLOG? | |
| Jun 2, 2015 at 22:40 | comment | added | tomasz | @AlexRavsky: Wow, thanks. Consistency of the negative answer is enough, as far as I am concerned. I might be interested in the special case where $H$ is analytic in the sense that it can be obtained from compact sets through the Souslin operation. Maybe this will prove a better assumption than Borelness? Borel sets tend to be rather odd in non-second-countable spaces. | |
| Jun 2, 2015 at 19:13 | comment | added | Alex Ravsky | I am glad to inform you that an international group of mathematicians is trying to answer your question. :-) We obtained negative answers under some additional axiomatic assumptions (for instance, Martin Axiom) and we are trying to obtain a negative answer in ZFC. Also we are trying to obtain a positive answer when the group $H$ is Borel. | |
| May 29, 2015 at 4:02 | comment | added | tomasz | @Ashutosh: I'm afraid my experience with forcing is even more meager than my experience with compact groups. ;-) So I can't even imagine what you're saying. | |
| May 28, 2015 at 22:17 | comment | added | Ashutosh | By reals i meant $2^{\omega}$. Here's a test situation to ponder: add $\aleph_1$ random reals and let H be the group generated by them. Can you write H as a countable union of sets whose self-sums are nowhere dense? | |
| May 28, 2015 at 20:44 | comment | added | tomasz | @Ashutosh: The additive group of reals is not compact. If anything, a base example would be the circle group (or more generally, compact metrisable groups). And no, I don't know the answer even in this case. | |
| May 28, 2015 at 14:51 | comment | added | Ashutosh | Do you know the answer when G is the additive group of reals? | |
| May 25, 2015 at 9:39 | review | First posts | |||
| May 25, 2015 at 9:55 | |||||
| May 25, 2015 at 9:37 | history | asked | tomasz | CC BY-SA 3.0 |