Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 4 / 22G / a

The sequence $(f_n)$ is equicontinuous on $[0,1]$ when, for every $\epsilon >0$, there is a $\delta >0$ such thatfor every $n$. The Arzela-Ascoli theorem says that a uniformly bounded equicontinuous sequence of continuous real-valued functions on a compact interval has a uniformly convergent subsequence.