Balleans and \(G\)-spaces
type: Item
instance of: scholarly article
title: Balleans and \(G\)-spaces
zbMATH Open document ID: 1283.54007
author: O. Petrenko
author: Igor V. Protasov
published in: Ukrainian Mathematical Journal
publication date: 2013-01-03T00:00:00Z
review text: Ball structures were introduced by the second author in [Ukr. Math. J. 54, No. 6, 1027--1037 (2002); original in Ukr. Mat. Zh. 54, No. 6, 847--855 (2002; Zbl 1003.05053)]. Let us quote the abstract of the paper: ``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 \(\mathcal U\) is a \(Q\)-point.'' Then the authors give some comments and several open questions in Section 3.
Mathematics Subject Classification ID: 54A20
zbMATH DE Number: 6121530
zbMATH Keywords: ballean
zbMATH Keywords: support
zbMATH Keywords: ultrafilters
zbMATH Keywords: \(T\)-point
zbMATH Keywords: \(P\)-point
zbMATH Keywords: \(Q\)-point
MaRDI profile type: Publication
full work available at URL: s11253-012-0653-x
OpenAlex ID: W2056734709
cites work: Balleans of topological groups
cites work: Embedding Theorems for Groups
cites work: Thin ultrafilters
cites work: Balleans of bounded geometry and G-spaces
cites work: Q3503958
cites work: Q4437801
DOI: 10.1007/S11253-012-0653-X
description: scientific article; zbMATH DE number 6121530