Protasov, Igor V. Balleans of bounded geometry and \(G\)-spaces. (English) Zbl 1164.37302 Algebra Discrete Math. 2008, No. 2, 101-108 (2008). Summary: 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 \(X\). Cited in 1 ReviewCited in 13 Documents MSC: 37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) 54E15 Uniform structures and generalizations Keywords:ballean; coarse equivalence; G-space PDFBibTeX XMLCite \textit{I. V. Protasov}, Algebra Discrete Math. 2008, No. 2, 101--108 (2008; Zbl 1164.37302)