1. The Baire category theorem - Aarhus Universitet

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Proof of Baire’s category theorem - continued The proof is now completed as follows; first the case when S is a locally compact Hausdorff space: B0 ⊇ B1 ⊇ B2 ⊇ B3 ⊇ ... and each Bk,k ≥ 1, is compact and non-empty. It follows that ∞ k=1 Bk = ∅. Since Bk ⊆ Vk−1 for all k, we find that ∞ ∞ Vk. k=1 Bk ⊆ k=0 Klaus Thomsen 1. The Baire category theorem
Proof of Baire’s category theorem - continued The proof is now completed as follows; first the case when S is a locally compact Hausdorff space: B0 ⊇ B1 ⊇ B2 ⊇ B3 ⊇ ... and each Bk,k ≥ 1, is compact and non-empty. It follows that ∞ k=1 Bk = ∅. Since Bk ⊆ Vk−1 for all k, we find that ∞ ∞ Vk. k=1 Bk ⊆ But ∞ k=1 Bk ⊆ B0, so we see that ∞ k=1 Bk ⊆ k=0 ∞ Vk ∩ B0, k=1 which was what we wanted to prove. 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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