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I really need help concerning this task: let $f : X \to \mathbb{R}^n$, $X\subseteq \mathbb{R}^n$, be a function with $X$ open.

Show: $f$ is continuous $\iff f^{-1} (W) $ is open for every open $W \subseteq\mathbb{R}^n$, when $f^{-1}$ is the inverse of $f$.

Thanks for your help.

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    I assume you're using the $\epsilon-\delta$ definition of continuity?2012-12-16
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    This is actually one of the definitions for continuity, so you really need to explain what definition you are using.2012-12-16
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    yes, we're using the definition icurays mentioned!2012-12-16
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    I don't think you want $f^{-1}$ to be the inverse. It might not exist.2012-12-16

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