Example 3

Tag 0B0M, permanent. Cite it as [Bourbaki, Tag 0B0M].

General Topology, chapter I, § 2. Continuous functions

Product topology. Let $(X_i)_{i \in I}$ be a family of topological spaces. The coarsest topology on the product set $X = \prod_{i \in I} X_i$ for which the projections $\mathrm{pr}_i : X \to X_i$ are continuous mappings is called the product of the topologies of the $X_i$ ; we shall study it in more detail in

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

Cited by

Proposition 7, § 2
Definition 1, § 4

Cites

Nothing.