Remark 3

Tag 01QY, permanent. Cite it as [Bourbaki, Tag 01QY].

Topologie algébrique, chapter I, § 5. Revêtements principaux

Let G be a locally compact group countable at infinity and let $G'$ be a separated topological group whose underlying space is a Baire space. Every continuous surjective homomorphism of G into $G'$ is open (TG, IX, p. 56, corollary and TG, III, p. 16, prop. 24).

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

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