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Locally dyadic topological groups

Published online by Cambridge University Press:  17 April 2009

Joan Cleary  and
Sidney A. Morris
Joan Cleary
Affiliation:
Department of MathematicsLa Trobe UniversityBundoora Vic 3083Australia
Sidney A. Morris
Affiliation:
Dept of Math Stats and Computing ScienceThe University of New EnglandArmidale NSW 2351Australia
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Abstract

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A topological space is said to be locally dyadic if every neighbourhood of a point contains a dyadic neighbourhood of that point. It is proved here that every locally compact Hausdorff topological group is locally dyadic.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 40 , Issue 3 , December 1989 , pp. 417 - 419
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Cleary, J. and Morris, S.A., ‘Topologies on locally compact groups’, Bull. Austral. Math. Soc. 38 (1988), 105–111.CrossRefGoogle Scholar
[2]Comfort, W. W., ‘Topological Groups’, in Handbook of Set-theoretic Topology, Kunen, K. and Vaughan, J. E. eds., pp. 1143–1264 (North-Holland, Amsterdam, 1984).CrossRefGoogle Scholar
[3]Engelking, R., ‘General Topology’, Polish Scientific Publishers Warsaw (1977).Google Scholar
[4]Hewitt, E. and Ross, K. A., Abstract Harmonic Analysis I (Springer-Verlag, Berlin, Heidelberg, New York, 1963).Google Scholar
[5]Kuz'minov, V., ‘On a hypothesis of P.S. Alexandroff in the theory of topological groups’, Dokl. Akad. Nauk SSSR 125 (1959), 727–729.Google Scholar
[6]Mostert, P.S., ‘Sections in principal fibre spaces’, Duke Math. J. 23 (1956), 57–71.CrossRefGoogle Scholar
[7]Price, J.F., Lie Groups and Compact Groups (Cambridge University Press, Cambridge, 1977).CrossRefGoogle Scholar
[8]van Douwen, E., ‘Problem L4’, Topology Proceedings 6 (1981), p. 441.Google Scholar