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CONTINUITY OF MULTIPLICATION IN THE LARGEST COMPACTIFICATION OF A LOCALLY COMPACT GROUP

Published online by Cambridge University Press:  14 June 2001

I. V. PROTASOV  and
J. S. PYM
I. V. PROTASOV
Affiliation:
Department of Cybernetics, State University of Kiev, Kiev, Ukraine; Kseniya@profit.net.ua
J. S. PYM
Affiliation:
Department of Pure Mathematics, University of Sheffeld, Sheffeld S3 7RH; j.pym@shef.ac.uk
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Abstract

G[Lscr ][Uscr ][Cscr ] is the largest semigroup compactification of the locally compact group G. When G is not compact, given q ∈ G* = G[Lscr ][Uscr ][Cscr ] \ G, there is p ∈ G* such that x [map ] qx is discontinuous at p (Theorem 2). If G is σ-compact, there is one p which will serve for all q (Theorem 1).

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 3 , May 2001 , pp. 279 - 282
Copyright
© The London Mathematical Society 2001

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Footnotes

This research was supported in part by the London Mathematical Society.