1. The Baire category theorem - Aarhus Universitet
1. The Baire category theorem - Aarhus Universitet
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>