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 \( \mathcal{I} \) 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 \( \mathcal{U} \) on ω is a T -point with respect to the class of all metrizable locally finite balleans on ω if and only if \( \mathcal{U} \) is a Q-point. The paper is concluded with a list of open questions.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 3, pp. 344–350, March, 2012.
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Petrenko, O.V., Protasov, I.V. Balleans and G-spaces. Ukr Math J 64, 387–393 (2012). https://doi.org/10.1007/s11253-012-0653-x
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DOI: https://doi.org/10.1007/s11253-012-0653-x