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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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$.


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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: http://dx.doi.org/10.1090/S0002-9939-07-08727-8
PII: S 0002-9939(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