Let $a,b\in\mathbb{R}$ with $a<b$. If $f:[a,b]\to\mathbb{R}$ is \reftext{def:continuity-closed-interval-c54-2026b}{continuous on $[a,b]$}, then $f$ is \reftext{def:uniform-continuity-real-subset-c54-2026a}{uniformly continuous} on $[a,b]$.