Proposition 9

Tag 0B5R, permanent. Cite it as [Bourbaki, Tag 0B5R].

General Topology, chapter I, § 7. Limits

A mapping $f$ of a topological space $X$ into a topological space $Y$ is continuous at a point $a \in X$ if and only if $\lim_{i \in I} f(x) = f(a)$ .

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

Cited by

Proposition 10, § 7
Corollary 1, § 7
Example 3, § 1
Remark, § 6
Proposition 10, § 2
Theorem 4, § 3

Cites

Nothing.