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1. The Baire category theorem - Aarhus Universitet

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On locally compact Hausdorff spaces<br />

Lemma<br />

Let X be a topological space.<br />

a) <strong>The</strong> union of a finite number of compact sets in X is itself<br />

compact.<br />

b) If K is a compact subset of X and B ⊆ K is a closed subset of<br />

K, then B is compact.<br />

Proof.<br />

a) is left to the reader.<br />

Klaus Thomsen <strong>1.</strong> <strong>The</strong> <strong>Baire</strong> <strong>category</strong> <strong>theorem</strong>

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