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. Klaus Thomsen 1. The Baire category theorem
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. 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
Page 11 and 12: A subset A of S is nowhere dense wh
Page 13 and 14: A subset A of S is nowhere dense wh
Page 21 and 22: Basic properties the notions of cat
Page 31: Basic properties the notions of cat
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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Proof of Baire’s category theorem
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1. The Baire category theorem - Aarhus Universitet

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