Proposition 5

Tag 0B2I, permanent. Cite it as [Bourbaki, Tag 0B2I].

General Topology, chapter I, § 4. Product of topological spaces

The projection of an open set $U$ of the product $X_1 \times X_2$ onto either factor is an open set.

For example, we have $\mathrm{pr}_2 U = \bigcup_{x_1 \in X_1} U(x_1)$ , and the proposition follows from the Corollary to Proposition 4 and axiom (O_1).

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

Cited by

Proposition 13, § 11
Proposition 3, § 4
Example 4, § 5
Corollary 1, § 1

Cites

Corollary to Proposition 4