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Semigroup Compactifications of Direct and Semidirect Products

Published online by Cambridge University Press:  20 November 2018

Paul Milnes
Paul Milnes*
Affiliation:
Department of Mathematics, The University of Western OntarioLondon, Ontario, CanadaN6A 5B7
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Abstract

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A classical result of I. Glicksberg and K. de Leeuw asserts that the almost periodic compactification of a direct product S × T of abelian semigroups with identity is (canonically isomorphic to) the direct product of the almost periodic compactiflcations of S and T. Some efforts have been made to generalize this result and recently H. D. Junghenn and B. T. Lerner have proved a theorem giving necessary and sufficient conditions for an F-compactification of a semidirect product S⊗σT to be a semidirect product of compactiflcations of S and T. A different such theorem is presented here along with a number of corollaries and examples which illustrate its scope and limitations. Some behaviour that can occur for semidirect products, but not for direct products, is exposed

Keywords

22A1522A2043A60semitopological semigroup(semidirect) product(right topological) compactification
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 2 , 01 June 1983 , pp. 233 - 240
Copyright
Copyright © Canadian Mathematical Society 1983

References

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