TY - JOUR AU - O. V. Petrenko AU - I. V. Protasov PY - 2012/03/25 Y2 - 2024/03/28 TI - Balleans and <i>G</i> -spaces JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 64 IS - 3 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2580 AB - 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. ER -