Closed Box in $\mathbb{R}^n$ is Compact

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 closed box determined by these endpoints. Then $B$ is compact in $\mathbb{R}^n$, where $\mathbb{R}^n$ is regarded as a topological space through the topology determined by the Euclidean distance.