On hyperballeans of bounded geometry

Abstract

A ballean (or coarse structure) is a set endowed with some family of subsets, the balls, in such a way that balleans with corresponding morphisms can be considered as asymptotic counterparts of uniform topological spaces. For a ballean $${{\mathscr {B}}}$$ on a set X, the hyperballean $${{\mathscr {B}}}^{\flat }$$ is a ballean naturally defined on the set $$X^{\flat }$$ of all bounded subsets of X. We describe all balleans with hyperballeans of bounded geometry and analyze the structure of these hyperballeans.