Corollary 2

Tag 0B6A, permanent. Cite it as [Bourbaki, Tag 0B6A].

General Topology, chapter I, § 8. Hausdorff spaces and regular spaces

If $f$ is a continuous mapping of a topological space $X$ into a Hausdorff space $Y$ , then the graph of $f$ is closed in $X \times Y$ .

For this graph is the set of all $(x, y) \in X \times Y$ such that $f(x) = y$ , and the two mappings $(x, y) \to y$ and $(x, y) \to f(x)$ are continuous.

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

Cited by

Proposition 5, § 10
Proposition 7, § 4
Proposition 9, § 6
Exercise 7, § 1

Cites

Nothing.