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On the classification of Polish metric spaces up to isometry


About this Title

Su Gao and Alexander S. Kechris

Publication: Memoirs of the American Mathematical Society
Publication Year 2003: Volume 161, Number 766
ISBNs: 978-0-8218-3190-8 (print); 978-1-4704-0364-5 (online)
DOI: http://dx.doi.org/10.1090/memo/0766
MathSciNet review: 1950332
MSC (2000): Primary 03E15; Secondary 54E35, 54H05

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Table of Contents


Chapters

  • Introduction
  • 1. Preliminaries
  • 2. Isometric classification of Polish metric spaces
  • 3. Characterizing the isometry groups of Polish metric spaces
  • 4. Some special cases
  • 5. Isometries of locally compact spaces, : The pseudo-connected case
  • 6. Isometries of locally compact spaces, : The general case
  • 7. Isometric classification of locally compact spaces
  • 8. Locally compact ultrametric spaces
  • 9. Some analogies with the model theory of countable structures
  • 10. Open problems