Balleans of bounded geometry and G-spaces

Abstract

A ballean (or a coarse structure) is a set endowed with some family of subsets which are called the balls. The properties of the family of balls are postulated in such a way that a ballean can be considered as an asymptotical counterpart of a uniform topological space.

We prove that every ballean of bounded geometry is coarsely equivalent to a ballean on some set \(X\) determined by some group of permutations of \(X\).