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Given that $A$ is an open set in $\mathbb R^n$ and $f:A \to \mathbb R^n$ is differentiable, and its derivative is non-singular at every point in $A$, prove that $f(A)$ is open in $\mathbb R^n$

Note $f$ is differentiable, not continuously differentiable.

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    Note that the tag "open-problem" is for problems for which no solution is known, *not* for problems concerning open sets.2012-03-21

2 Answers 2