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I am not able to solve this problem:

Prove that if $f:M\rightarrow N$ is $C^{\infty}$, one-to-one, onto, and everywhere non-singular, then $f$ is a diffeomorphism.

This $f$ is a diffeomorphism $\iff$ $df$ is surjective everywhere, right? Then how to proceed?

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    Dear Matt, Iam simply pleased and delighted at your suggestion.Collecting Lee and starting reading it :)2012-06-29

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