1996/12/05 by Howard S. Becker, Alexander S. Kechris · 2 citations
Mathematics · #Advanced Topology and Set Theory #Mathematics #Group action #Ergodic theory #Pure mathematics #Topological group #Equivalence relation #Group (periodic table) #Algebra over a field #Invariant (physics) #Locally compact space #Polish space #Topological dynamics #Congruence relation #Lie group #Group theory #Orbit (dynamics) #Topology (electrical circuits) #Topological tensor product #Combinatorics #Mathematical analysis
paper · doi:10.1017/cbo9780511735264
openalex publication_date 1996/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02
In this book the authors present their research into the foundations of the theory of Polish groups and the associated orbit equivalence relations. The particular case of locally compact groups has long been studied in many areas of mathematics. Non-locally compact Polish groups occur naturally as groups of symmetries in such areas as logic (especially model theory), ergodic theory, group representations, and operator algebras. Some of the topics covered here are: topological realizations of Borel measurable actions; universal actions; applications to invariant measures; actions of the infinite symmetric group in connection with model theory (logic actions); dichotomies for orbit spaces (including Silver, Glimm-Effros type dichotomies and the topological Vaught conjecture); descriptive complexity of orbit equivalence relations; definable cardinality of orbit spaces.