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> - continued<br />
Finally the completion of the proof in the case of a complete metric<br />
space:<br />
As above B0 ⊇ B1 ⊇ B2 ⊇ B3 ⊇ ... and ∞<br />
It remains therefore only to show that ∞<br />
k=1 Bk = ∅.<br />
k=1 Bk ⊆ ∞ k=0 Vk ∩B0.<br />
Klaus Thomsen <strong>1.</strong> <strong>The</strong> <strong>Baire</strong> <strong>category</strong> <strong>theorem</strong>