Corollary 1

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

If $Y$ is a complete uniform space, then $C_u(X; Y)$ is complete.

For, by Theorem 2, $C_u(X; Y)$ is a closed uniform subspace of the uniform space $F_u(X; Y)$ , which is complete by Theorem 1 of no. 5.

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

Cited by

Nothing.