Let $n\in\mathbb{N}$, let $U\subseteq \mathbb{R}^n$, and let $d_E$ be the \reftext{def:euclidean-distance-rn-2026a}{Euclidean distance} on $\mathbb{R}^n$. Then $U$ is \reftext{def:open-subset-euclidean-space-2026a}{open in the Euclidean sense} if and only if $U$ is \reftext{def:open-subset-metric-space-2026a}{open in the metric space $(\mathbb{R}^n,d_E)$}.