Arzela-Ascoli theorem
= Arzelà-Ascoli theorem
{c}
{wiki=Arzelà–Ascoli_theorem}
For a compact Hausdorff space $K$, a subset of $C(K)$ is relatively compact in the uniform norm exactly when it is <equicontinuous> and pointwise bounded. On a compact metric space, this says that every uniformly bounded equicontinuous sequence has a uniformly convergent subsequence.