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Jun 28 at 12:04 comment added David Roberts Oh, that is a nice way to think about it, thanks for clarifying.
Jun 28 at 7:32 comment added Sergiy Maksymenko Yes, exactly. The reason of that formulation is that in the paper we look at the classification of C^k structures on M as a description of orbits of the action of homeomorphisms of M on the set of C^k structures.
Jun 28 at 7:09 comment added David Roberts I guess the conclusion of your statement in italics could instead be "there exists a $C^k$-diffeomorphism $h\colon U\to \mathbb{R}$"?
Jun 27 at 16:44 history edited LSpice CC BY-SA 4.0
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Jun 27 at 16:14 history edited Sergiy Maksymenko CC BY-SA 4.0
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Jun 27 at 16:03 history answered Sergiy Maksymenko CC BY-SA 4.0