Balleans and G -spaces

• Date: 2012
• Main Authors: Petrenko, O. V., Protasov, I. V., Петренко, О. В., Протасов, І. В.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2012
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2580
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 uniform...