Question

What is a uniformly continuous function?

Answer 1

A uniformly continuous function is a function that, given any two points in its domain, can be made as close as desired by making the distance between the two points sufficiently small. This means that the function is continuous and its graph is a single, unbroken line.

Answer 2

Informally, a continuous function satisfying the weierstrass definition of limits in the same way, regardless of the point in the function.

Formally, for all \(\varepsilon>0\) there exists a \(\delta>0\) such that for all \(x, y \in X|x-y|<\delta\) implies \(|f(x)-f(y)|<\varepsilon\)