Uniform closure of a function algebra
= Uniform closure of a function algebra
= Uniform closure
{synonym}
For an algebra $A\subseteq C(K)$ on a compact space, its uniform closure consists of functions that are <uniform limits> of sequences from $A$. It is a closed algebra in the <uniform norm>, because addition and multiplication preserve uniform convergence for bounded functions. If it contains every constant and separates points, the <Stone-Weierstrass theorem> makes the closure all of $C(K)$.