1. The Baire category theorem - Aarhus Universitet

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On locally compact Hausdorff spaces Before we continue the proof of Baire’s category theorem we develop a little of the general theory of locally compact Hausdorff spaces. Recall that a topological space is locally compact when every point has an open neighborhood with compact closure. Klaus Thomsen 1. The Baire category theorem
On locally compact Hausdorff spaces Before we continue the proof of Baire’s category theorem we develop a little of the general theory of locally compact Hausdorff spaces. Recall that a topological space is locally compact when every point has an open neighborhood with compact closure. Lemma Let X be a Hausdorff space, K a compact subset of X and p a point in the complement K c = X \K of K. There are then open sets U and W such that p ∈ U,K ⊆ W and U ∩ W = ∅. 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
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Page 35 and 36: Proof of the corollary Reminder ?:
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1. The Baire category theorem - Aarhus Universitet

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