Minimal actions of the group $ {\Bbb S(Z)} $ of permutations of the integers

85 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

THE UNIVERSAL MINIMAL SYSTEM FOR THE GROUP OF HOMEOMORPHISMS OF THE CANTOR SET (2003, methodology): “However, whereas in [3] the main combinatorial tool was the well known Ramsey theorem, here we use one of the consequences of Graham”
SOME EXTREMELY AMENABLE GROUPS RELATED TO OPERATOR ALGEBRAS AND ERGODIC THEORY (2004, background): “While surely not all infinite dimensional groups are extremely amenable, the fixed point on compacta property of subgroups can be used to make conclusions about the dynamical properties of larger groups, for instance, to describe their universal minimal compact flows [48, 20 ].”
More on the Kechris-Pestov-Todorcevic correspondence: precompact expansions (2012, background): “few cases were known to be both metrizable and non-trivial, the most important examples being provided by the orientation-preserving homeomorphisms of the circle (Pestov, [Pes98]), S∞ (Glasner-Weiss, [GW02]), and the homeomorphism group of the Cantor space (Glasner-Weiss, [GW03]). In that context, t”
Fraïssé Limits, Ramsey Theory, and topological dynamics of automorphism groups (2003, methodology): “The first such example is in Pestov [64], where the author shows that the universal minimal flow of H+(T), the group of orientation preserving homeomorphisms of the circle, has as a universal minimal flow its natural (evaluation) action on T. Then Glasner-Weiss [ 30 ] showed that the universal minim”