Definition:Uniform Equivalence/Metric Spaces

Definition
Let $M_1 = \struct {A_1, d_1}$ and $M_2 = \struct {A_2, d_2}$ be metric spaces.

Then the mapping $f: A_1 \to A_2$ is a uniform equivalence of $M_1$ with $M_2$ $f$ is a bijection such that $f$ and $f^{-1}$ are both uniformly continuous.