Polish Metric Spaces: Their Classification and Isometry Groups
colorful horizontal rule

John D. Clemens, Su Gao and Alexander S. Kechris

Abstract(preliminary)

This is an announcement of research results on the classification problems of Polish metric spaces and on their isometry groups.

This paper attempts to give a coherent account of the main results of an earlier joint paper of Gao and Kechris and a part of Clemens' PhD dissertation. In addition, some new results about the classification of rigid, ultrahomogeneous, and/or discrete spaces are given (without proof).

Table of Contents

  1. Introduction
  2. The Classification of General Polish Metric Spaces
  3. The Classification of Special Classes of Polish Metric Spaces
    1. Ultrametric and zero-dimensional spaces
    2. Homogeneous, ultrahomogeneous and rigid spaces
    3. Locally compact spaces
  4. Groups of Isometries
  5. Open Problems
    References

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