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I would like to find a function $F:\mathbb{R}^N\to\mathbb{R}^N$, for $N\geq 2$, which is surjective and a local diffeomorphism, but which is not injective. I can solve the problem by using partition of unity, but I would like to find an explicit example.

Any help is appreciated.

CJD
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Tomás
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  • Any such $F$ can't be proper, otherwise it would be a covering map which would have to be the identity map as $\mathbb{R}^N$ is its own universal cover. – Michael Albanese Jul 26 '15 at 21:58

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