Balleans and G -spaces - Petrenko, O. V.; Protasov, I. V. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
We show that every ballean (equivalently, coarse structure) on a set X can be determined by some group G of permutations of X and some group ideal I on G. We refine this characterization for some basic classes of balleans: metrizable, cellular, graph, locally finite, and uniformly locally finite. Then we show that a free ultrafilter U on ω is a T-point with respect to the class of all metrizable locally finite balleans on ω if and only if U is a Q-point. The paper is concluded with а list of open questions.