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My professor stated (but did not prove) the Baire category theorem as follows: "If (X,d) is a complete metric space, then for any sequence F_n of closed sets whose reunion is X, there is a k such that the interior of F_k is non-empty.

How is this equivalent to the more traditional statement " If (X,d) is a complete metric space, then for any sequence F_n of closed sets with empty interior, their reunion has empty interior as well."

???

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# Homework Help: Baire category theorem

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