Proposition 6

Tag 0CF9, permanent. Cite it as [Bourbaki, Tag 0CF9].

General Topology, chapter X, § 4. Approximation of continuous real-valued functions

Let $X$ be a compact space and let $H$ be a set of continuous real-valued functions on $X$ which separates the points of $X$ . Then every continuous mapping of $X$ into a normed space $Y$ over $\mathbf{R}$ can be uniformly approximated by polynomials in the functions of $H$ with coefficients in $Y$ .

From this we deduce:

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

Cited by

Proposition 7, § 4

Cites

Nothing.