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On theorems of Thornton

Published online by Cambridge University Press:  17 April 2009

R. Lalithambal
R. Lalithambal
Affiliation:
Department of Mathematics, Madurai University, Madurai, Tamil Nadu, India.
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Abstract

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The topology of a topological group in which the intersection of open sets is open is uniquely determined by a normal subgroup, and the group is uniquely an extension of an indiscrete group by a discrete group. This was proved by M.C. Thornton under the additional hypothesis that the group is a torsion group. The proofs here given make the more general facts almost trivial.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 6 , Issue 2 , April 1972 , pp. 211 - 212
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Hewitt, Edwin and Ross, Kenneth A., Abstract harmonic analysis, Vol. I (Die Grundlehren der mathematischen Wissenschaften, Band 115. Academic Press, New York; Springer-Verlag, Berlin, Göttingen, Heidelberg, 1963).Google Scholar
[2]Thornton, M.C., “Torsion topological groups with minimal open sets”, Bull. Austral. Math. Soc. 5 (1971), 55–59.CrossRefGoogle Scholar