Proposition 26

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

General Topology, chapter III, § 2. Subgroups, quotient groups, homomorphisms homogeneous spaces, product groups

The bijection of $X/G$ onto $\prod_{i \in I} (X_i/G_i)$ canonically associated with $(\varphi_i)$ is a homeomorphism. For since the $\varphi_i$ are surjective and open, it follows that $\varphi = (\varphi_i)$ is an open mapping (Chapter I, , no. 3, Corollary to Proposition 8)

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

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