Definition:Uniform Equivalence/Metrics

Definition
Let $A$ be a set on which there are two metrics imposed: $d_1$ and $d_2$.

Then $d_1$ and $d_2$ are uniformly equivalent iff the identity mapping of $A$ is uniformly $\left({d_1, d_2}\right)$-continuous and also uniformly $\left({d_2, d_1}\right)$-continuous.