Let $(X,d)$ be a [metric space](/page/Metric%20Space), let $x_0 \in X$, and let $r > 0$. Define the closed ball of radius $r$ centered at $x_0$ by $\overline{B}(x_0,r) := \{y \in X : d(y,x_0) \leq r\}$. If $(x_k)_{k \in \mathbb{N}}$ is a sequence in $\overline{B}(x_0,r)$ and $x_k \to x$ in the metric space $(X,d)$, then $x \in \overline{B}(x_0,r)$.