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Compact metrizable groups are isometry groups of compact metric spaces

Author(s): Julien Melleray
Journal: Proc. Amer. Math. Soc. 136 (2008), 1451-1455.
MSC (2000): Primary 54H11; Secondary 22A05, 51F99
Posted: December 28, 2007
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Abstract: This note is devoted to proving the following result: given a compact metrizable group , there is a compact metric space such that is isomorphic (as a topological group) to the isometry group of .

References:

1.: H.Becker and A.S Kechris, The Descriptive Set Theory of Polish Group Actions, London Math. Soc. Lecture Notes Series, 232, Cambridge University Press (1996). MR 1425877 (98d:54068)
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)
3.: M. Katětov, On universal metric spaces, Proc. of the 6th Prague Topological Symposium (1986), Frolik (ed). Helderman Verlag, Berlin, pp. 323-330 (1988). MR 0952617 (89k:54066)


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