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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Proof of <strong>Baire</strong>’s <strong>category</strong> <strong>theorem</strong><br />
Let V1,V2,V3,... be open and dense subsets of S. We must show<br />
that ∞ i=1 Vi is dense in S when S is either a complete metric<br />
space or a locally compact Hausdorff space.<br />
Klaus Thomsen <strong>1.</strong> <strong>The</strong> <strong>Baire</strong> <strong>category</strong> <strong>theorem</strong>