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Isometry groups of separable metric spaces

Published online by Cambridge University Press:  01 January 2009

MACIEJ MALICKI  and
SŁAWOMIR SOLECKI
MACIEJ MALICKI
Affiliation:
Department of Mathematics, 1409 W. Green Street, University of Illinois, Urbana, IL 61801, USA. e-mail: [email protected]; [email protected]
SŁAWOMIR SOLECKI
Affiliation:
Department of Mathematics, 1409 W. Green Street, University of Illinois, Urbana, IL 61801, USA. e-mail: [email protected]; [email protected]
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Abstract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 1 , January 2009 , pp. 67 - 81
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

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