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Polish Metric Spaces: Their Classification and Isometry Groups

2001
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Bulletin of Symbolic Logic
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§ 1. Introduction. In this communication we present some recent results on the classification of Polish metric spaces up to isometry and on the isometry groups of Polish metric spaces. A Polish metric space is a complete separable metric space (X, d). Our first goal is to determine the exact complexity of the classification problem of general Polish metric spaces up to isometry. This work was motivated by a paper of Vershik [1998], where he remarks (in the beginning of Section 2): "The

doi:10.2307/2687754
fatcat:j5kabnrlzra7rnpfhu5hepvu6y