Dini continuity
In mathematical analysis, Dini continuity is a refinement of continuity. Every Dini continuous function is continuous. Every Lipschitz continuous function is Dini continuous.Definition
Let be a compact subset of a metric space, and let be a function from into itself. The modulus of continuity of is
The function is called Dini-continuous if
An equivalent condition is that, for any,
where is the diameter of.
