naa a22 4500 510781551 CHVBK 20180411083249.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1007/s11854-013-0010-5 doi (NATIONALLICENCE)springer-10.1007/s11854-013-0010-5 Minimal hyperspace actions of homeomorphism groups of h-homogeneous spaces [Elektronische Daten] [Eli Glasner, Yonatan Gutman] Suppose that X is an h-homogeneous zero-dimensional compact Hausdorff space, i.e., X is a Stone dual of a homogeneous Boolean algebra. Using the dual Ramsey theorem and a detailed combinatorial analysis of what we call stable collections of subsets of a finite set, we obtain a complete list of the minimal sub-systems of the compact dynamical system (Exp(Exp(X)), Homeo(X)), where Exp(X) denotes the hyperspace comprising the closed subsets of X equipped with the Vietoris topology. The importance of this dynamical system stems from Uspenskij's characterization of the universal ambit of G = Homeo(X). The results apply to the Cantor set, the generalized Cantor sets X = {0,1} κ for noncountable cardinals κ, and to several other spaces. A particular interesting case is X = ω* = βω \ ω, where βω denotes the Stone- Čech compactification of the natural numbers. This space, called the corona or the remainder of ω, has been extensively studied in the fields of set theory and topology. Hebrew University Magnes Press, 2013 Glasner Eli School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, 69978, Tel Aviv, Israel aut Gutman Yonatan Laboratoire d'Analyse et de Mathématiques Appliquées, Université de Marne-la-Valle, 5 Boulevard Descartes Cité Descartes — Champs-sur-Marne, 77454, Marne-la-Valle cedex 2, France aut Journal d'Analyse Mathématique The Hebrew University Magnes Press 119/1(2013-04-01), 305-332 0021-7670 119:1<305 2013 119 11854 https://doi.org/10.1007/s11854-013-0010-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11854-013-0010-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Glasner Eli School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, 69978, Tel Aviv, Israel aut NATIONALLICENCE 700 1- Gutman Yonatan Laboratoire d'Analyse et de Mathématiques Appliquées, Université de Marne-la-Valle, 5 Boulevard Descartes Cité Descartes — Champs-sur-Marne, 77454, Marne-la-Valle cedex 2, France aut NATIONALLICENCE 773 0- Journal d'Analyse Mathématique The Hebrew University Magnes Press 119/1(2013-04-01), 305-332 0021-7670 119:1<305 2013 119 11854 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer