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CONTINUITY OF MEASURABLE HOMOMORPHISMS

Part of: Connections with other structures, applications Topological and differentiable algebraic systems

Published online by Cambridge University Press:  01 August 2008

JANUSZ BRZDȨK
JANUSZ BRZDȨK*
Affiliation:
Department of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland (email: [email protected])
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Abstract

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We give some general results concerning continuity of measurable homomorphisms of topological groups. As a consequence we show that a Christensen measurable homomorphism of a Polish abelian group into a locally compact topological group is continuous. We also obtain similar results for the universally measurable homomorphisms and the homomorphisms that have the Baire property.

Keywords

Christensen measurabilityBaire propertyuniversal measurabilityHaar measurabilitymeasurable homomorphism of groups

MSC classification

Secondary: 22A05: Structure of general topological groups 39B52: Equations for functions with more general domains and/or ranges 54H11: Topological groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 1 , August 2008 , pp. 171 - 176
Copyright
Copyright © 2008 Australian Mathematical Society

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