Proposition 3

Tag 0C77, permanent. Cite it as [Bourbaki, Tag 0C77].

General Topology, chapter IX, § 5. Baire spaces

Every non-empty open subspace $Y$ of a Baire space $X$ is a Baire space.

This follows from (EB"), for every open (resp. meagre) set in $Y$ is open (resp. meagre) in $X$ .

It follows from Proposition 3 that every point of a Baire space has a fundamental system of neighbourhoods, each of which is a Baire space. Conversely:

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Theorem 2, § 5

Cites

Nothing.