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Suppose $ i \in [0,1]$ and for each $i$, $X_i$ is a compact metric space. Then, is it that a Cartesian product of $X_i$ over $ i \in [0,1]$ is also a compact metric space?

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    Are you the same user as the one which asked http://math.stackexchange.com/questions/85783/constructing-a-convergent-subsequence2011-12-25

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