Let $a,b\in\mathbb{R}$ satisfy $a\le b$. Then the interval $[a,b]$ from \reftext{def:interval-real-line-c54-2026c}{the interval definition} is \reftext{def:compact-space-and-subset-2026a}{compact in $\mathbb{R}$}, where $\mathbb{R}$ is regarded as a topological space through the topology determined by the \reftext{def:euclidean-distance-rn-2026a}{Euclidean distance}.