Baire's lemma in complete metric spaces
Topology and measurement

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Baire's lemma in complete metric spaces


Topology and measurement

Author : Gilles GODEFROY

Publication date: April 10, 2003 | Lire en français

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3. Baire's lemma in complete metric spaces

The following lemma was proved by R. Baire, in the context of spaces n , shortly before 1900. Baire's proof extends easily to the general case.

A part D of a metric space E is dense if D¯=E , or equivalently if any non-empty open of E meets D.

Lemma 1: Let (E,

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