1. The Baire category theorem - Aarhus Universitet

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Proof of Baire’s category theorem - continued Finally the completion of the proof in the case of a complete metric space: As above B0 ⊇ B1 ⊇ B2 ⊇ B3 ⊇ ... and ∞ It remains therefore only to show that ∞ k=1 Bk = ∅. k=1 Bk ⊆ ∞ k=0 Vk ∩B0. Klaus Thomsen 1. The Baire category theorem
Proof of Baire’s category theorem - continued Finally the completion of the proof in the case of a complete metric space: As above B0 ⊇ B1 ⊇ B2 ⊇ B3 ⊇ ... and ∞ k=1 Bk ⊆ ∞ k=0 Vk ∩B0. It remains therefore only to show that ∞ Choose xk ∈ Bk. We claim that {xk} ∞ k=1 k=1 Bk = ∅. is a Cauchy sequence in S. Klaus Thomsen 1. The Baire category theorem
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1. The Baire category theorem Klaus
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We read in W. Rudin: Functional Ana
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Definition of first and second cate
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A subset A of S is nowhere dense wh
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A subset A of S is nowhere dense wh
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Basic properties the notions of cat
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1. The Baire category theorem - Aarhus Universitet

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