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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
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Abstract

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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