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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeApr 4th 2021
• (edited Apr 4th 2021)

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.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeApr 4th 2021
• (edited Apr 4th 2021)

at coset space it is claimed (I guess this was myself) that the proof for compact Lie subgroups is due to

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeApr 4th 2021

changed page name from “… with local sections” to “… admitting local sections”

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeApr 4th 2021

changed page name to singular

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTime1 day ago

I have added pointer to Section 3 of

• Takashi Karube, On the local cross-sections in locally compact groups, J. Math. Soc. Japan 10(4): 343-347 (October, 1958) (doi:10.2969/jmsj/01040343)

for mentioning of one and a half counter-examples.

Any larger collection of counter-examples out there?