Open Access
2016 Turning Automatic Continuity Around: Automatic Homomorphisms
Ryan M. Berndt, Greg G. Oman
Real Anal. Exchange 41(2): 271-286 (2016).


Let $G$ and $H$ be Polish groups and let $\pi\colon G\rightarrow H$ be a function. The automatic continuity problem is the following: assuming $\pi$ is a group homomorphism, find conditions on $G$, $H$, or $\pi$ which imply that $\pi$ is continuous. In this note, we initiate a study of a reverse problem: supposing $\pi$ is continuous, find conditions on $G$, $H$, or $\pi$ which imply that $\pi$ is a homomorphism. Herein, we treat the case $G=H=\mathbb{R}$.


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Ryan M. Berndt. Greg G. Oman. "Turning Automatic Continuity Around: Automatic Homomorphisms." Real Anal. Exchange 41 (2) 271 - 286, 2016.


Published: 2016
First available in Project Euclid: 30 March 2017

zbMATH: 1384.22002
MathSciNet: MR3730718

Primary: 22A05 , 26A15
Secondary: 20F38

Keywords: ‎automatic continuity , Homomorphism , lattice , Polish group

Rights: Copyright © 2016 Michigan State University Press

Vol.41 • No. 2 • 2016
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