Metrizable ball structures

I. V. Protasov

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.

ball structure, ball isomorphism, metrizablility