Past exam of the mathematics course of the University of Oxford / 2015 / Prelims / Mathematics II / 4 / a / i

A function $f:E\to \mathbb{R}$ is continuous on $E$ if it is continuous at every $p\in E$, meaningThe function has uniform continuity on $E$ whenFor continuity, $\delta$ may depend on both $p$ and $\epsilon$. For uniform continuity, one $\delta$ must work for every pair of points in $E$.