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5d41402abc4
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 Benefactor
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Diffeomorphism of an open set and almost all of $\mathbb{R}^n$
@FallenApart Yes, that is correct.
awarded
 Promoter
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Diffeomorphism of an open set and almost all of $\mathbb{R}^n$
@Neal Yes, those are the correct quantifiers.
awarded
 Student
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Diffeomorphism of an open set and almost all of $\mathbb{R}^n$
I'm not sure I understand your counter-example. It seems to me like you could smoothly deform the union of two disjoint sets into $\mathbb{R}$ so that the set where you don't have a diffeomorphism is measure zero. Could you add further details?
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 Editor
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Diffeomorphism of an open set and almost all of $\mathbb{R}^n$
Yes, I edited the header.
revised
Diffeomorphism of an open set and almost all of $\mathbb{R}^n$
added 6 characters in body
asked
Diffeomorphism of an open set and almost all of $\mathbb{R}^n$