[分析] Baire Category Theorem

[tsaihohan (有人想一起下圍棋嗎)]

        We say that a closed subset C of a metric space X

        is nowhere-dense if and only if C contains no non

        -empty open subset of X. Prove the Baire Category

        Theorem: When X is a complete metric space, there

        does not exist a countable collection

        {C_γ包含於X：γ屬於Ν} of nowhere-dense closed subsets

        of X satisfying X = ∪C_γ, γ屬於Ν.



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