Let $n\in\mathbb{N}$. For each index $i\in\{1,\dots,n\}$, let $a_i,b_i\in\mathbb{R}$ satisfy $a_i\le b_i$, and let $B\subseteq\mathbb{R}^n$ be the \reftext{def:closed-box-rn-2026a}{closed box} determined by these endpoints. Then $B$ is \reftext{def:compact-space-and-subset-2026a}{compact in $\mathbb{R}^n$}, where $\mathbb{R}^n$ is regarded as a topological space through the topology determined by the \reftext{def:euclidean-distance-rn-2026a}{Euclidean distance}.