Isometry groups of separable metric spaces

MacIej Malicki, Sławomir Solecki

Research output: Contribution to journalArticlepeer-review


We show that every locally compact Polish group is isomorphic to the isometry group of a proper separable metric space. This answers a question of Gao and Kechris. We also analyze the natural action of the isometry group of a separable ultrametric space on the space. This leads us to a structure theorem representing an arbitrary separable ultrametric space as a bundle with an ultrametric base and with ultrahomogeneous fibers which are invariant under the action of the isometry group.

Original languageEnglish (US)
Pages (from-to)67-81
Number of pages15
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number1
StatePublished - Jan 2009

ASJC Scopus subject areas

  • General Mathematics


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