Balleans and <i>G</i> -spaces

  • O. V. Petrenko Kyiv. Nat. Taras Shevchenko Univ.
  • I. V. Protasov Kyiv Nat. Taras Shevchenko Univ.

Abstract

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.
Published
25.03.2012
How to Cite
PetrenkoO. V., and ProtasovI. V. “Balleans and <i>G</I&gt; -Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 3, Mar. 2012, pp. 344-50, http://umj.imath.kiev.ua/index.php/umj/article/view/2580.
Section
Research articles