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I need to prove:

Let $A$ be open in $\mathbb{R}^m$, $g:A \longrightarrow \mathbb{R}^n$ a locally lipschitz function and $C$ a compact subset of $A$.

Show that $g$ is lipschitz on $C$.

Can anyone help me?

  • 1
    Very similar: http://math.stackexchange.com/questions/154391/locally-lipschitz-implies-lipschitz So, possible duplicate?2012-06-06
  • 6
    @Weltschmerz The proof on $\mathbb R$ used the order structure which isn't available here.2012-06-06

3 Answers 3