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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Extension of a theorem of Baayen and Helmberg on monothetic groups


Author: D. L. Armacost
Journal: Proc. Amer. Math. Soc. 96 (1986), 502-504
MSC: Primary 22A05
DOI: https://doi.org/10.1090/S0002-9939-1986-0822449-8
MathSciNet review: 822449
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Abstract: Let $G$ and $K$ be compact monothetic groups and let $\phi$ be a continuous homomorphism from $G$ onto $K$. If $k$ is a generator of $K$, must there exist a generator $g$ of $G$ such that $\phi \left ( g \right ) = k?$? A useful theorem of Baayen and Helmberg provides an affirmative answer if $K$ is the circle $T$. We show that the answer remains affirmative as long as $K$ is metrizable. We also provide an example to show that the answer may be negative for nonmetrizable $K$.


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Keywords: Monothetic, generator
Article copyright: © Copyright 1986 American Mathematical Society