\begin{definition}[Definition:Lipschitz Equivalence/Terminology]
Despite the close connection with the concept of Lipschitz continuity, this concept is rarely seen in mainstream mathematics, and appears not to have a well-established name.
The name '''Lipschitz equivalence''' appears in {{BookReference|Introduction to Metric and Topological Spaces|1975|W.A. Sutherland}}:
:''There does not appear to be a standard name for this; the name we use is reasonably appropriate ...''
Sometimes the name '''strong equivalence''' (and '''strongly equivalent metrics''') is used.
{{Namedfor|Rudolf Lipschitz}}
\end{definition}