Abstract
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 $G=H=\mathbb{R}$.
Citation
Ryan M. Berndt. Greg G. Oman. "Turning Automatic Continuity Around: Automatic Homomorphisms." Real Anal. Exchange 41 (2) 271 - 286, 2016.
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