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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- © Copyright 1986 American Mathematical Society
- 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