Remark 1

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

General Topology, chapter X, § 1. The uniformity of $\mathscr{G}$-convergence

In general, the set $\mathscr{C}(X; Y)$ is not closed in $\mathscr{F}(X; Y)$ with respect to the topology of pointwise convergence: in other words, a pointwise limit of continuous functions is not necessarily continuous [Exercise 5 a)].

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

Cited by

Nothing.

Cites

Exercise 5