- #1

Euge

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Suppose $f : \Bbb R^n \to \Bbb R^m$ is a differentiable function such that the derivative $Df$ has constant rank $n$. If $\Omega \subset \Bbb R^n$ is bounded, prove that to every $y\in \Bbb R^m$ there corresponds only finitely many solutions to the equation $f(x) = y$ in $\Omega$.

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