Geodesic
Metrizable ball structures
Algebra and discrete mathematics, no. 1 (2002), pp. 129-141.

Voir la notice de l'article provenant de la source Math-Net.Ru

A ball structure is a triple (X,P,B), where X, P are nonempty sets and, for any x∈X, α∈P, B(x,α) is a subset of X, x∈B(x,α), which is called a ball of radius α around x. We characterize up to isomorphism the ball structures related to the metric spaces of different types and groups.
Mots-clés : ball structure, ball isomorphism, metrizablility. 
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I. V. Protasov. Metrizable ball structures. Algebra and discrete mathematics, no. 1 (2002), pp. 129-141. https://geodesic-test.mathdoc.fr/item/ADM_2002_1_a7/