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

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A claim of Gromov in "Metric Structures for Riemannian and non-Riemannian Spaces" [closed]

I'm trying to understand an example that occurs very early in Gromov's book "Metric Structures for Riemannian and Non-Riemannian Spaces". On page 3, he introduces the following metric on $\mathbb{R}^n …
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