Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-05-24T22:16:30.598Z Has data issue: false hasContentIssue false
  • English
  • Français

A characterization of the topological group of real numbers

Published online by Cambridge University Press:  17 April 2009

Sidney A. Morris
Sidney A. Morris
Affiliation:
La Trobe University, Bundoora, Victoria 3083, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that a non-discrete locally compact Hausdorff group has each of its proper closed subgroups finite (respectively, discrete) if and only if it is topologically isomorphic to the circle group (respectively, the circle group or the group of real numbers).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 3 , December 1986 , pp. 473 - 475
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Armacost, David L., The Structure of Locally Compact Abelian Groups (Marcel Dekker, Inc., New York, 1981).Google Scholar
[2]Hewitt, Edwin and Ross, Kenneth A., Abstract Harmonic Analysis I (Springer-Verlag, Berlin, 1963).Google Scholar
[3]Isiwata, T., “On the connectedness of locally compact groups”, Sci. Rep. Tokyo kyoiky Daigaku, Sect. A5 (1955) 8–13.Google Scholar
[4]Morris, Sidney A., Pontryagin Duality and the Structure of Locally Compact Abelian Groups (Cambridge University Press, Cambridge, 1977).CrossRefGoogle Scholar
[5]Price, John F., Lie Groups and Compact Groups (Cambridge University Press, 1977).CrossRefGoogle Scholar
[6]Robertson, L.C. and Schreiber, B.M., “The additive structure of integer groups and p-adic number fields”, Proc. Amer. Math. Soc. 19 (1968) 1453–1456.Google Scholar