The Cantor set of linear orders on N is the universal minimal S_\infty-system
| dc.creator | Glasner, Eli | |
| dc.date | 2002-04-10 | |
| dc.date.accessioned | 2026-07-07T04:47:34Z | |
| dc.date.available | 2026-07-07T04:47:34Z | |
| dc.description | Each topological group $G$ admits a unique universal minimal dynamical system $(M(G),G)$. When $G$ is a non-compact locally compact group the phase space $M(G)$ of this universal system is non-metrizable. There are however topological groups for which $M(G)$ is the trivial one point system (extremely amenable groups), as well as topological groups $G$ for which $M(G)$ is a metrizable space and for which there is an explicit description of the dynamical system $(M(G),G)$. One such group is the topological group $S_\infty$ of all permutations of the integers ${\mathbb Z}$, with the topology of pointwise convergence. We show that $(M(S_\infty),S_\infty)$ is a symbolic dynamical system (hence in particular $M(S_\infty)$ is a Cantor set), and give a full description of all its symbolic factors. Among other facts we show that $(M(G),G)$ (and hence also every minimal $S_\infty$) has the structure of a two-to-one group extension of proximal system and that it is uniquely ergodic. | |
| dc.description | 5 pages. The results in this article will be treated fully in an article, written jointly with B. Weiss, to be published in Geometric and Functional Analysis (GAFA) | |
| dc.identifier | https://arxiv.org/abs/math/0204126 | |
| dc.identifier | http://arxiv.org/abs/math/0204126 | |
| dc.identifier | Proceedings of the Ninth Prague Topological Symposium, (Prague, 2001), pp. 119--123, Topology Atlas, Toronto, 2002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63769 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 22A05, 22A10, 54H20 | |
| dc.title | The Cantor set of linear orders on N is the universal minimal S_\infty-system | |
| dc.type | text |