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- Jun 20, 2014

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Let $f : X \to Y$ be a closed map of topological spaces such that the fibers $f^{-1}(y)$ are compact for every $y\in Y$. Prove that $f$ is a proper map, i.e., $f^{-1}(K)$ is a compact subset of $X$ for every compact subset $K$ of $Y$.

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