Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-28T18:06:34.841Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
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.

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