Metric Spaces

By Iii ) X = R

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Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness (2020, methodology): “From the mathematical point of view, this is equivalent to requiring h to satisfy the bi-Lipschitz condition [65]:”
On Hilbert's fourth problem (2013, methodology): “(We recall that Busemann developed a theory of convexity in general metric spaces, see [38] and the exposition in [88].”
On the asymptotic magnitude of subsets of Euclidean space (2009, background): “Lawvere observed [6] that the first two of these conditions are analogous to composition of morphisms and the inclusion of the identity in a category: Hom(x, x′)×Hom(x′, x′′)→ Hom(x, x′′) and {∗} → Hom(x, x).”