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I have no idea how to show whether this statement is false or true:

If every differentiable function on a subset $X\subseteq\mathbb{R}^n$ is bounded then $X$ is compact.

Thank you

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    $\textbf{Hint:}$ Think about how one can characterize compact subsets of $\mathbb{R}^n$. Suppose that $X$ is not compact and try to find a differentiable function on $X$ that isn't bounded.2012-12-12

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