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Locally compact topologies on abelian groups

Published online by Cambridge University Press:  24 October 2008

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

It is shown that an abelian group admits a non-discrete locally compact group topology if and only if it has a subgroup algebraically isomorphic to the group of p-adic integers or to an infinite product of non-trivial finite cyclic groups. It is also proved that an abelian group admits a non-totally-disconnected locally compact group topology if and only if it has a subgroup algebraically isomorphic to the group of real numbers. Further, if an abelian group admits one non-totally-disconnected locally compact group topology then it admits a continuum of such topologies, no two of which yield topologically isomorphic topological groups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 2 , March 1987 , pp. 233 - 235
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

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