A function f: X -> Y is uniformly continuous if and only if for every ε > 0, there exists a δ > 0 such that d_Y(f(x),f(y)) < ε for all x,y in X with d_X(x,y) < δ.
A function f: X -> Y is uniformly continuous if and only if for every ε > 0, there exists a δ > 0 such that d_Y(f(x),f(y)) < ε for all x,y in X with d_X(x,y) < δ.