1. The Baire category theorem - Aarhus Universitet

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Definition of first and second category Second category A set A ⊆ S is of second category when it is not of the first category. Via the Baire category theorem we will become able to give many examples - for example show that R is of the second category as a subset of itself. (As well as [0,1] ⊆ R). Klaus Thomsen 1. The Baire category theorem
Definition of first and second category Second category A set A ⊆ S is of second category when it is not of the first category. Via the Baire category theorem we will become able to give many examples - for example show that R is of the second category as a subset of itself. (As well as [0,1] ⊆ R). Subsequently we shall then see why the notion is usefull ! Philosophically a set of second category is a large subset of S from the topological point of view. 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 17: Definition of first and second cate
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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