Uniform Continuity
- Mathematics & Logic -
Pure Mathematics Dictionary
Definition
Global version of continuity: a function f on a domain D is uniformly continuous if for every ε>0 there exists a single δ>0 such that for all x,y in D, d(x,y)<δ implies d(f(x),f(y))<ε. The key is that δ depends only on ε, not on the point.