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Compact metrizable groups are isometry groups of compact metric spaces


Author: Julien Melleray
Journal: Proc. Amer. Math. Soc. 136 (2008), 1451-1455
MSC (2000): Primary 54H11; Secondary 22A05, 51F99
DOI: https://doi.org/10.1090/S0002-9939-07-08727-8
Published electronically: December 28, 2007
MathSciNet review: 2367119
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Abstract: This note is devoted to proving the following result: given a compact metrizable group $ G$, there is a compact metric space $ K$ such that $ G$ is isomorphic (as a topological group) to the isometry group of $ K$.


References [Enhancements On Off] (What's this?)

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  • 2. S. Gao and A.S Kechris, On the classification of Polish metric spaces up to isometry, Memoirs of Amer. Math. Soc., 766, Amer. Math. Soc. (2003). MR 1950332 (2004b:03067)
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Additional Information

Julien Melleray
Affiliation: Université Paris 6, Boîte 186, 4 Place Jussieu, Paris Cedex 05, France
Email: melleray@math.jussieu.fr

DOI: https://doi.org/10.1090/S0002-9939-07-08727-8
Received by editor(s): January 10, 2006
Received by editor(s) in revised form: March 7, 2006
Published electronically: December 28, 2007
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2007 American Mathematical Society

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