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Licensed Unlicensed Requires Authentication Published by De Gruyter May 17, 2012

Separable ultrametric spaces and their isometry groups

  • Maciej Malicki EMAIL logo
From the journal Forum Mathematicum
An erratum for this article can be found here: https://doi.org/10.1515/forum-2015-0050

Abstract

The paper is devoted to a study of isometry groups of Polish ultrametric spaces. We explicitly describe isometry groups of spaces that are non-locally rigid and satisfy the property that distances between orbits under the action of the isometry group are realized by points. The type of group construction appearing here is a variant of the generalized wreath product. We prove that it has a natural universality and uniqueness property. As an application, we characterize Polish ultrametric spaces satisfying the above properties, whose isometry groups have uncountable strong cofinality.

Funding source: Marie Curie IRG

Award Identifier / Grant number: REDUCE 224808

Received: 2011-12-3
Revised: 2012-4-17
Published Online: 2012-5-17
Published in Print: 2014-11-1

© 2015 by De Gruyter

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