Timeline for A question regarding the action of a Lie subgroup
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 13, 2021 at 4:09 | vote | accept | A beginner mathmatician | ||
| Jan 12, 2021 at 3:45 | history | edited | LSpice | CC BY-SA 4.0 |
Proofreading while this is on the front page
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| Jan 12, 2021 at 2:25 | answer | added | Jack Lee | timeline score: 5 | |
| Dec 11, 2020 at 5:59 | comment | added | A beginner mathmatician | @Ramiro. Aha! That's what I meant in my question. Thank for confirming this. | |
| Dec 9, 2020 at 23:28 | comment | added | Ramiro Lafuente | Lee defines Lie subgroups as subgroups endowed with some topology and smooth structure that makes them immersed submanifolds. So the argument in the book has a gap, as it is implicitly assuming that H is an embedded submanifold. It appears that the "closed subgroup theorem" should have been proved before the result that you are quoting, as it is done for instance in the book of Warner, Foundations of Differentiable Manifolds and Lie groups. | |
| Dec 6, 2020 at 20:52 | comment | added | Liviu Nicolaescu | Try this with $H=\mathbb{Z}$ and $G=(\mathbb{R},+)$ | |
| Dec 6, 2020 at 13:07 | comment | added | YCor | The question is a bit unclear. If your starting point is a closed subgroup and you're asking why the "topology on $H$" is the same as the subspace topology, you seem to assume that $H$ is given another topology... but this is not part of the setting. Maybe your starting point is that $H$ is a Lie group (with assumptions??) with an injective homomorphism with closed image into $G$ and you're asking whether this is a homeomorphism onto its image. Whether this holds, depends on the assumptions... | |
| Dec 6, 2020 at 12:49 | comment | added | A beginner mathmatician | @Zero. Please read the question clearly and then comment. | |
| Dec 6, 2020 at 11:18 | comment | added | user130903 | The topology of $H$ is the subspace topology. | |
| Dec 6, 2020 at 9:44 | history | asked | A beginner mathmatician | CC BY-SA 4.0 |