Automatic continuity of measurable homomorphisms on Cech-complete topological groups

2022/06/06 by Banakh, Taras · 1 citation
#03E15 #03E75 #22A10 #22D05 #28A05 #54C05 #54C08 #54D45 #54E52 #54H05 #54H11 #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2206.02481

Abstract

We prove that a homomorphism h:X→ Y from a (locally compact) Cech-complete topological group X to a topological group Y is continuous if and only if h is Borel-measurable if and only if h is universally measurable (if and only if h is Haar-measurable). This answers a problem of Kuznetsova and extends a result of Kleppner on the continuity of Haar-measurable homomorphisms between locally compact groups and a result of Rosendal on the continuity of universally measurable homomorphisms between Polish groups.

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