1. The Baire category theorem - Aarhus Universitet

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A subset A of S is nowhere dense when the closure A has empty interior. Reminder: The closure A of A is by definition the intersection of the closed sets containing A. The interior of any subset B ⊆ X is the union of the open sets contained in B. Thus a subset A of S is nowhere dense when the closure A does not contain any open subset. Klaus Thomsen 1. The Baire category theorem
A subset A of S is nowhere dense when the closure A has empty interior. Reminder: The closure A of A is by definition the intersection of the closed sets containing A. The interior of any subset B ⊆ X is the union of the open sets contained in B. Thus a subset A of S is nowhere dense when the closure A does not contain any open subset. Examples: The integers Z is nowhere dense in R. The set { 1 n : n ∈ N} is nowhere dense [0,1]. Klaus Thomsen 1. The Baire category theorem
Page 1 and 2: 1. The Baire category theorem Klaus
Page 3 and 4: We read in W. Rudin: Functional Ana
Page 5 and 6: Definition of first and second cate
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Page 21 and 22: Basic properties the notions of cat
Page 33 and 34: The Baire’s category theorem The
Page 35 and 36: Proof of the corollary Reminder ?:
Page 41 and 42: Proof of Baire’s category theorem
Page 47 and 48: On locally compact Hausdorff spaces
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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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