Definition:Uniform Equivalence/Metric Spaces

Definition
Let $M_1 = \left({A_1, d_1}\right)$ and $M_2 = \left({A_2, d_2}\right)$ be metric spaces.

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