Let $n \in \mathbb{N}$, let $x_0 \in \mathbb{R}^n$, and let $r > 0$. In $\mathbb{R}^n$ with the Euclidean metric, the topological closure of the open ball $B(x_0,r)$ is the closed ball $\overline{B}(x_0,r)$; that is, $\overline{B(x_0,r)} = \overline{B}(x_0,r)$.