1. The Baire category theorem - Aarhus Universitet

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On locally compact Hausdorff spaces Proof. Since X is locally compact we can, for each k ∈ K, find an open set Wk such that k ∈ Wk and Wk is compact. Since {Wk : k ∈ K} is an open cover of K, and K is compact, there is a finite collection k1,k2,...,kN such that K ⊆ Wk1 ∪ Wk2 ∪ · · · ∪ WkN . Set W = Wk1 ∪ Wk2 ∪ · · · ∪ WkN and note that W ⊆ Wk1 ∪ Wk2 ∪ · · · ∪ WkN . Klaus Thomsen 1. The Baire category theorem
On locally compact Hausdorff spaces Proof. Since X is locally compact we can, for each k ∈ K, find an open set Wk such that k ∈ Wk and Wk is compact. Since {Wk : k ∈ K} is an open cover of K, and K is compact, there is a finite collection k1,k2,...,kN such that K ⊆ Wk1 ∪ Wk2 ∪ · · · ∪ WkN . Set W = Wk1 ∪ Wk2 ∪ · · · ∪ WkN and note that W ⊆ Wk1 ∪ Wk2 ∪ · · · ∪ WkN . It follows from Lemma 3 that W is compact. This completes the proof in the case where U = X, since we can then take V = W. 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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A subset A of S is nowhere dense wh
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1. The Baire category theorem - Aarhus Universitet

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