Uniform Continuity

definitionreal-analysis

Definition

A function $f:I\to \mathbb{R}$, for an interval $I$, is called uniformly continuous on $I$ if $\forall \epsilon >0$, there exists $\delta >0$ so that $|f(x)-f(y)|<\epsilon$ for all $x,y\in I$, such that $|x-y|<\delta$.

Differs from Continuity

Examples