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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.

2 votes

Mapping in reference to a metric space (terminology question)

I'm not certain that all of the conditions you mention in your "definition" are satisfied in this setting, but I think you should look at $\Gamma$-Ultrametric spaces, c.f. notes by Ackerman, where $\G …
Jeremy LeCrone's user avatar