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

8 votes

Is there an algebraic approach to metric spaces?

I guess this is not the expected kind of answer, but you can study a metric space as a category, enriched over $\mathbb{R}_+$ - a monoidal category of non-negative real numbers (with $\infty$) with na …
Anton Fetisov's user avatar