\begin{definition}[Definition:Lipschitz Equivalence/Metric Spaces]
Let $M_1 = \struct {A_1, d_1}$ and $M_2 = \struct {A_2, d_2}$ be metric spaces.
Let $f: M_1 \to M_2$ be a mapping such that $\exists h, k \in \R_{>0}$ such that:
:$\forall x, y \in A: h \map {d_2} {\map f x, \map f y} \le \map {d_1} {x, y} \le k \map {d_2} {\map f x, \map f y}$
Then $f$ is a '''Lipschitz equivalence''', and $M_1$ and $M_2$ are  described as '''Lipschitz equivalent'''.
\end{definition}