Solution
= Solution
A family $F$ of <continuous functions> on a <compact space> $K$ is <equicontinuous family of functions>[equicontinuous] if, for every $x$ and every $ε>0$, there is a neighbourhood $U$ of $x$ such that $|f(y)-f(x)|<ε$ for every $y$ in $U$ and every $f$ in $F$. The <Arzelà-Ascoli theorem> says that $F$ has compact closure in $C(K)$ with the <uniform norm> if and only if it is equicontinuous and pointwise bounded.