1. The Baire category theorem - Aarhus Universitet

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The Baire’s category theorem The Baire’s category theorem. If S is either (a) a complete metric space, or (b) a locally compact Hausdorff space, then the intersection of every countable collection of dense open sets in S is dense is S. Thus if Ei,i = 1,2,3,... , are dense and open in S, then ∞ i=1 Ei is dense in S. Corollary. A complete metric space or a locally compact Hausdorff space is of the second category; thus they are not the union of a countable collection of nowhere dense subsets. Klaus Thomsen 1. The Baire category theorem
Proof of the corollary Reminder ?: A subset E of S is dense when E ∩ U = ∅ for all open and non-empty subsets U. Klaus Thomsen 1. The Baire category theorem
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Proof of Baire’s category theorem
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1. The Baire category theorem - Aarhus Universitet

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