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How to prove this exercise?

Let $f$ be a continuous function of $\mathbb R^n$ to $\mathbb R^m$, so that $f^{-1}(B)$ is compact in $\mathbb R^n$ for all compact $B$ in $\mathbb R^m$. Prove that $f(A)$ is a closed set in $\mathbb R^m$ for all closed set $A$ in $\mathbb R^n$.

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    Do not change the question and title completely. Ask a new question.2011-09-17
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    @Andres Please do not change the question so substantially that you invalidate the current answers completely. If you want to ask a question about sequences, ask a fresh question; **please do not edit the existing question on topology to ask this**.2011-09-17

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