Uniform_continuity

Definition

A function $f:A \rightarrow \mathbb{R}$ is uniformly continuous on $A$ if for every $\epsilon > 0$ there exists a $\delta > 0$ such that for all $x,y \in A$, $|x - y| < \delta$ implies $|f\left. (x) \right. - f\left. (y) \right. < \epsilon$.