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Aug 20, 2021 at 20:39 comment added Steven Stadnicki @AchimKrause That's a great intuitive example.
Aug 20, 2021 at 10:08 comment added Achim Krause As an explicit example, I like $SO(3)$ with $a,b$ two rotations by the same angle around two different axes which are very close to each other. For any $m$, $a^m$ and $b^m$ will still be two rotations by the same angle around those axes, thus close to each other.
Aug 20, 2021 at 6:39 comment added free your answer is true . your may also is true for SIN-group. Particular, Thanks you
Aug 20, 2021 at 6:32 history answered Dmitry Vaintrob CC BY-SA 4.0