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 $x\in X$, $\alpha\in P$, $B(x,\alpha)$ is a subset of $X$, $x\in B(x,\alpha)$, which is called a ball of radius $\alpha$ around $x$. We characterize up to isomorphism the ball structures related to the metric spaces of different types and groups.
Keywords: ball structure, ball isomorphism, metrizablility. 
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     author = {I. V. Protasov},
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I. V. Protasov. Metrizable ball structures. Algebra and discrete mathematics, no. 1 (2002), pp. 129-141. http://geodesic.mathdoc.fr/item/ADM_2002_1_a7/