Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-02-03T12:04:21.782Z Has data issue: false hasContentIssue false
  • English
  • Français

The circle group

Published online by Cambridge University Press:  17 April 2009

Sidney A. Morris
Sidney A. Morris
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Victoria, 3083Australia.
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.

We prove the following theorem: if G is a locally compact Hausdorff group such that each of its proper closed subgroups has only a finite number of closed subgroups, then G is topologically isomorphic to the circle group.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 2 , October 1987 , pp. 279 - 282
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Armacost, David L., The Structure of Locally Compact Abelian Groups, (Marcel Dekker, New York, 1981).Google Scholar
[2]Bröcker, Theodor and Dieck, Tammo tom, Representations of Lie Groups, (Springer-Verlag, New York, 1985).CrossRefGoogle Scholar
[3]Hewitt, Edwin and Ross, Kenneth A., Abstract Harmonic Analysis I (Springer-Verlag, Berlin, 1963).Google Scholar
[4]Morris, Sidney A., Pontryagin Duality and the Structure of Locally Compact Abelian Groups (Cambridge University Press, Cambridge, 1977).CrossRefGoogle Scholar
[5]Morris, Sidney A., “A characterization of the topological group of real numbers”, Bull. Austral. Math. Soc. 34, (1986) 473–475.CrossRefGoogle Scholar