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) has a neighborhood basis at the identity consisting of open subgroups 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).
Generic Element Isometry Group Open Subgroup Partial Isometry Incoming Edge
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