Let $S$ be a set, let $(Y,e)$ be a [metric space](/page/Metric%20Space), and let $f_k:S\to Y$ for $k\in\mathbb N$ and $f:S\to Y$ be functions. If $f_k$ converges uniformly to $f$ on $S$, then for every $s\in S$, the sequence $(f_k(s))_{k\in\mathbb N}$ converges to $f(s)$ in the metric space $(Y,e)$.