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Certain semigroups embeddabable in topological groups

Part of: Abstract harmonic analysis Topological and differentiable algebraic systems

Published online by Cambridge University Press:  09 April 2009

Heneri A. M. Dzinotyiweyi
Heneri A. M. Dzinotyiweyi
Affiliation:
Department of Mathematics University of ZimbabweP. O. Box MP 167 Mount Pleasant, Salisbury, Zimbabwe
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Abstract

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In this paper we study commutative topological semigroups S admitting an absolutely continuous measure. When S is cancellative we show that S admits a weaker topology J with respect to which (S, J) is embeddable as a subsemigroup with non-empty interior in some locally compact topological group. As a consequence, we deduce certain results related to the existence of invariant measures on S and for a large class of locally compact topological semigroups S, we associate S with some useful topological subsemigroup of a locally compact group.

MSC classification

Secondary: 22A20: Analysis on topological semigroups 43A05: Measures on groups and semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 1 , August 1982 , pp. 30 - 39
Copyright
Copyright © Australian Mathematical Society 1982

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