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On the Classification of Polish Metric Spaces Up to Isometry
Su Gao, University of North Texas, Denton, TX, and Alexander S. Kechris, California Institute of Technology, Pasadena, CA

Memoirs of the American Mathematical Society
2003; 78 pp; softcover
Volume: 161
ISBN-10: 0-8218-3190-9
ISBN-13: 978-0-8218-3190-8
List Price: US$57
Individual Members: US$34.20
Institutional Members: US$45.60
Order Code: MEMO/161/766
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Graduate student and research mathematicians.

Table of Contents

  • Introduction
  • Preliminaries
  • Isometric classification of Polish metric spaces
  • Characterizing the isometry groups of Polish metric spaces
  • Some special cases
  • Isometries of locally compact spaces, I: The pseudo-connected case
  • Isometries of locally compact spaces, II: The general case
  • Isometric classification of locally compact spaces
  • Locally compact ultrametric spaces
  • Some analogies with the model theory of countable structures
  • Open problems
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