Let $n\in\mathbb{N}$ and let $U\subseteq \mathbb{R}^n$. Then $U$ is \reftext{def:open-subset-euclidean-space-2026a}{open in the Euclidean sense} if and only if for every point $x=(x_1,\dots,x_n)\in U$ there exists a real number $\delta>0$ such that every point $y=(y_1,\dots,y_n)\in\mathbb{R}^n$ satisfying

for every $i\in\{1,\dots,n\}$ belongs to $U$.