TY - JOUR
AU - O. V. Petrenko
AU - I. V. Protasov
PY - 2012/03/25
Y2 - 2023/03/29
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 -