1. The Baire category theorem - Aarhus Universitet

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Definition of first and second category First category A set A ⊆ S is of first category if it is the union of a countable collection of nowhere dense sets, i.e. if A = ∞ i=1 Ai, where Ai have empty interior. Klaus Thomsen 1. The Baire category theorem
Definition of first and second category First category A set A ⊆ S is of first category if it is the union of a countable collection of nowhere dense sets, i.e. if A = ∞ i=1 Ai, where Ai have empty interior. Example: The rational numbers Q form a set of first category in the real line R. Note that Q itself is not nowhere dense; but it is the union of a countable collection of sets that are! Klaus Thomsen 1. The Baire category theorem
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Page 3 and 4: We read in W. Rudin: Functional Ana
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Page 41 and 42: Proof of Baire’s category theorem
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On locally compact Hausdorff spaces
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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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