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am giving this its own entry, in order to record sufficient conditions on topological subgroup inclusions $H \subset G$ for the coset space coprodoction $G \to G/H$ to admit local sections.
So far I have two original references here (Gleason 50, Mostert 53). One should add some textbook account, too.
Am also referencing this at closed subgroup, at coset space and maybe elsewhere.
at coset space it is claimed (I guess this was myself) that the proof for compact Lie subgroups is due to
But scanning through this article now, I haven’t spotted yet where that statement would appear in this article.
I have added pointer to Section 3 of
for mentioning of one and a half counter-examples.
Any larger collection of counter-examples out there?
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