Ends of graphed equivalence relations. II
type: Item
instance of: scholarly article
title: Ends of graphed equivalence relations. II
zbMATH Open document ID: 1167.03031
author: Greg Hjorth
author: Benjamin D. Miller
published in: Israel Journal of Mathematics
publication date: 2009-02-17T00:00:00Z
review text: For Part I see [\textit{B. D. Miller}, Isr. J. Math. 169, 375--392 (2009; Zbl 1166.03026)]. Given a graphing \(G\) of a countable Borel equivalence relation on a Polish space, the authors show that if there is a~Borel way of selecting a non-empty closed set of countably many ends from each \(G\)-component, then there is a Borel way of selecting an end or line from each \(G\)-component. Their method yields also Glimm-Effros-style dichotomies that characterize the circumstances under which: (1) there is a Borel way of selecting a point or end from each \(G\)-component; and (2) there is a Borel way of selecting a point, end or line from each \(G\)-component.
reviewed by: Denis I. Saveliev
Mathematics Subject Classification ID: 03E15
Mathematics Subject Classification ID: 54H05
zbMATH DE Number: 5508746
zbMATH Keywords: countable Borel equivalence relations
zbMATH Keywords: graphings of equivalence relations
zbMATH Keywords: dichotomies
Wikidata QID: Q56989846
MaRDI profile type: Publication
full work available at URL: s11856-009-0016-y
OpenAlex ID: W4243643036
cites work: Ergodic Equivalence Relations, Cohomology, and Von Neumann Algebras. I
cites work: COUNTABLE BOREL EQUIVALENCE RELATIONS
cites work: Q4323294
cites work: Topics in orbit equivalence
DOI: 10.1007/S11856-009-0016-Y
description: scientific article; zbMATH DE number 5508746