Let be uniform spaces, and a continuous function. If is compact, then is uniformly continuous.
For instance, if is a continuous function, then it is uniformly continuous.
![$ f: [a,b] \rightarrow \mathbb{R}$](http://images.planetmath.org:8080/cache/objects/3066/l2h/img5.png "$ f: [a,b] \rightarrow \mathbb{R}$"){kind=small}