2013/12/23 by Maciej Malicki, Malicki, Maciej
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #Characterization (materials science) #Class (philosophy) #Combinatorics #Computer science #Conjugacy class #FOS: Mathematics #Group (periodic table) #Group Theory (math.GR) #Isometry (Riemannian geometry) #Isometry group #Mathematics #Metric space #Physics #Pure mathematics #Sequence (biology) #Space (punctuation) #Transfinite number #Ultrametric space #advanced mathematical theories #math.GR
paper · pdf · doi:10.48550/arxiv.1312.6563
openalex publication_date 2013/12/23 · arxiv created 2015/04/15 · arxiv updated 2015/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This paper presents a study of generic elements in full isometry groups of Polish ultrametric spaces. We obtain a complete characterization of Polish ultrametric spaces X whose isometry group Iso(X) contains an open subgroup H with ample generics. It also gives a characterization of the existence of an open subgroup in Iso(X) with a comeager conjugacy class. We also study the transfinite sequence defined by the projection of a Polish ultrametric space X on the ultrametric space of orbits of X under the action of Iso(X).