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並前往https://mathoverflow.net/questions/204027/when-a-homeomorphism-is-a-diffeomorphism-w-r-t-to-a-suitable-smooth-structure

When a homeomorphism is a diffeomorphism wrt to a suitable ...

Let me first answer your last question in the negative: there exist homeomorphisms f:M→M of smoothable manifolds M such that neither f nor f−1 are smooth ...

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