Polish metric spaces: Their classification and isometry groups

Bulletin of Symbolic Logic

Volumn 7, Issue 3, 2001, Pages 361-375

  Clemens, John D ^a   Gao, Su ^b   Kechris, Alexander S ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035600116     PISSN: 10798986     EISSN: None     Source Type: Journal    
DOI: 10.2307/2687754     Document Type: Article

References (20)

1. H. BECKER AND A. S. KECHRIS [1996], The descriptive set theory of Polish group actions, London Mathematical Society Lecture Note Scries, vol. 232, Cambridge University Press.
2. J. D. CLEMENS [2001], Ph.D. thesis, University of California, Berkeley.
3. R. DOUGHERTY, S. JACKSON, AND A.S. KECHRIS [1994], The structure of hyperfinite Borel equivalence relations, Transactions of the American Mathematical Society, vol. 341, no. 1, pp. 193-225.
4. S. GAO AND A. S. KECHRIS [2000], On the classification of Polish metric spaces up to isometry, preprint.
5. M. GROMOV [1999], Metric structures for Riemannian and non-Riemannian spaces, Progress in Mathematics, vol. 152, Birkhäuser.
6. G. HJORTH [2000], Classification and orbit equivalence relations, Mathematical Surveys and Monographs, vol. 75. American Mathematical Society.
7. G. HJORTH AND A.S. KECHRIS [1996]. Borel equivalence relations and classifications of countable models, Annals of Pure and Applied Logic, vol. 82, pp. 221-272.
8. M. KATĚTOV [1988], On universal metric spaces. General topology and its relations to modern analysis and algebra, VI (Prague, 1986), Research and Exposition in Mathematics, vol. 16, Heldermann, Berlin, pp. 323-330.
9. A. S. KECHRIS [1995], Classical descriptive set theory, Springer-Verlag.
10. A. S. KECHRIS [1999], New directions in descriptive set theory, this BULLETIN, vol. 5, no. 2, pp. 161-179.
11. A. S. KECHRIS [2001], Actions of Polish groups and classification problems, Analysis and logic, London Mathematical Society Lecture Notes Series. Cambridge University Press, to appear.
12. A. MANOUSSOS AND P. STRANTZALOS [2000], The role of connectedness in the structure and the action of groups of isometrics of locally compact metric spaces, preprint.
13. Z. SEMADENI [1971], Banach spaces of continuous functions, PWN Polish Scientific Publishers.
14. P. STRANTZALOS [1974], Dynamische Systeme und Topologische Aktionen, Manuscripta Mathematica, vol. 13, pp. 207-211.
15. P. STRANTZALOS [1989], Action by isometries, Transformation groups (Osaka 1987), Lecture Notes in Mathematics, vol. 1375, Springer, pp. 319-325.
16. P. URYSOHN [1927], Sur en espace métrique universel. Bulletin des Sciences Mathématiques, vol. 51, pp. 43-64, 74-90.
17. V. V. USPENSKIǏ [1986], A universal topological group with a countable basis, Functional Analysis and Its Applications, vol. 20, pp. 86-87.
18. V. V. USPENSKIǏ [1990], On the group of isometries of the Urysohn universal metric space, Commentationes Mathematicae Universitatis Carolinae, vol. 31, no. 1, pp. 181-182.
19. D. VAN DANTZIG AND B.L. VAN DER WAERDEN [1928], Über metrisch homogene Räume, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, vol. 6, pp. 374- 376.
20. A. M. VERSHIK [1998], The universal Urysohn space, Gromov metric triples and random metrics on the natural numbers, Russian Mathematical Surveys, vol. 53, no. 5, pp. 921-928.