Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-16T23:40:59.521Z Has data issue: false hasContentIssue false
  • English
  • Français

An example of a polish group

Published online by Cambridge University Press:  12 March 2014

Maciej Malicki
Maciej Malicki*
Affiliation:
University of Illinois at Urbana-Champaign, Department of Mathematics, 1409 W.Green ST, IL 61801. USA, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We construct a non-discrete Polish group none of whose non-discrete subgroups admits a complete left-invariant metric.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 4 , December 2008 , pp. 1173 - 1178
Copyright
Copyright © Association for Symbolic Logic 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Becker, H., Polish group actions: Dichotomies and generalized elementary embeddings, Journal of the American Mathematical Society, vol. 11 (1998), no. 2, pp. 397–449.CrossRefGoogle Scholar
[2]Cameron, P. J., Oligomorphic Permutation Group, London Mathematical Society Lecture Notes, vol. 152, Cambridge University Press, Cambridge, 1990.CrossRefGoogle Scholar
[3]Dieudonne, J., Sur la completion des groupes topologiques. Comptes Rendus de l'Académie des Sciences Paris, vol. 218 (1944), pp. 774–776.Google Scholar
[4]Dobrowolski, T. and Marciszewski, W., Covering a Polish group hy translates of a nowhere dense set, Topology and its Applications, (2006), to appear.Google Scholar
[5]Gao, S. and Ding, L., Graev metric groups and Polishahle subgroups. 2005, preprint.Google Scholar
[6]Hjorth, G., Cameron's cofinitary group conjecture, Journal of Algebra, vol. 200 (1998), no. 2, pp. 439–448.CrossRefGoogle Scholar