@article{Petrenko_Protasov_2012, title={Balleans and <i>G</i> -spaces}, volume={64}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2580}, abstractNote={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 $\omega$ is a $T$-point with respect to the class of all metrizable locally finite balleans on $\omega$ if and only if $\mathcal{U}$ is a $Q$-point. The paper is concluded with а list of open questions.}, number={3}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Petrenko, O. V. and Protasov, I. V.}, year={2012}, month={Mar.}, pages={344-350} }