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Balleans of bounded geometry and \(G\)-spaces. (English) Zbl 1164.37302

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 \(X\).

MSC:

37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
54E15 Uniform structures and generalizations
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