A function f :I → ℝ, defined on an interval I, is uniformly continuous if, for every ε‎>0, there exists a single δ‎ > 0 such that, for all x,y ε‎ I satisfying |y − x| < δ‎, then |f(y) − f(x)| < ε‎. For continuity only, the value of δ‎ typically depends on x as well as ε‎. The notion extends readily to metric spaces, and continuous functions on a compact space are uniformly continuous. Absolutely continuous functions are uniformly continuous, but the converse does not hold (see Cantor distribution).