Automatic continuity of measurable homomorphisms on Cech-complete topological groups

Autor:	Banakh, Taras
Rok vydání:	2022
Předmět:	Mathematics - General Topology Mathematics - Group Theory 03E15 03E75 22A10 22D05 28A05 54C05 54C08 54D45 54E52 54H05 54H11
Druh dokumentu:	Working Paper
Popis:	We prove that a homomorphism $h:X\to Y$ 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. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2206.02481 Zobrazit plný text záznamu View this record from Arxiv