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$M,N$ are two smooth $n$-manifolds and $A$ is a subset of $M$. A smooth mapping $f$ from $M$ to $N$ has the property that $df$ is nonsingular and $f$ is injective on $A$. Is there a neighbourhood $U$ of $A$ such that $f$ is a diffeomorphism from $U$ to its image?

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    Neighbourhood _containing_ A, or neighbourhood _contained_ in A? Actually, I think the answer either way is no...2012-03-20

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