Definition:Uniform Equivalence/Metric Spaces

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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 $M_2$ if and only if $f$ is a bijection such that $f$ and $f^{-1}$ are both uniformly continuous.


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