Let be $G$ a Lie group and $H \subset G$ a closed Lie subgroup. It's well known that the action of $H$ on $G$ is free and proper, but in this proof I cannot find where the author use the closeness of $H$. Any help?
2026-03-27 04:18:49.1774585129
Action of a closed Lie subgroup $H$ on $G$ is proper: why $H$ need to be closed?
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The author uses the fact that $H$ is closed to show that $ba^{-1}$ is an element of $H$ since $h_j$ is an element of $H$.