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Compact metrizable groups are isometry groups of compact metric spaces

Julien Melleray
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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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Julien Melleray. 2005-06-22. Compact metrizable groups are isometry groups of compact metric spaces. https://arxiv.org/abs/math/0505509

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