Timeline for A variation of closed-subgroup theorem
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| May 7, 2021 at 0:55 | comment | added | Robert Bryant | @SeanEberhard: Ah, you are right. Thanks for the explanation! | |
| May 6, 2021 at 22:17 | vote | accept | aglearner | ||
| May 6, 2021 at 21:40 | answer | added | Sean Eberhard | timeline score: 4 | |
| May 6, 2021 at 21:10 | comment | added | Sean Eberhard | @RobertBryant The problem is that the non-compact skew line still doesn't work, because its intersection with a nbd of 1 is dense there | |
| May 6, 2021 at 20:31 | comment | added | Robert Bryant | I'm not sure why the OP is modifying the question. In the original question, the OP did not ask that the Lie subgroup $G\subset \mathrm{SO}(n)$ be compact, i.e., closed, just that it exist, and the 'skew-line' that Sean writes down is obviously part of a (non-closed) Lie subgroup. Did the OP mean to require that $G$ be a closed Lie subgroup? | |
| May 6, 2021 at 16:29 | history | edited | aglearner | CC BY-SA 4.0 |
added 132 characters in body
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| May 6, 2021 at 16:24 | comment | added | aglearner | Dear Sean, thanks! This is indeed a counter-example, but it am not afraid of it. I'll modify the question so that there is still a meaning, which is good enough for me | |
| May 6, 2021 at 15:42 | comment | added | Sean Eberhard | What if (a trite example) $X = \{(x, \sqrt{2}x) : x \in [-\epsilon, \epsilon]\} \subset \mathbf{T}^2$ (and the torus is embedded in $\mathrm{SO}(n)$)? | |
| May 6, 2021 at 13:22 | history | edited | YCor | CC BY-SA 4.0 |
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| May 6, 2021 at 13:20 | history | asked | aglearner | CC BY-SA 4.0 |