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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Extension of a theorem of Baayen and Helmberg on monothetic groups
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by D. L. Armacost PDF
Proc. Amer. Math. Soc. 96 (1986), 502-504 Request permission


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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  • P. C. Baayen and G. Helmberg, On families of equi-uniformly distributed sequences in compact spaces, Math. Ann. 161 (1965), 255–278. MR 188188, DOI 10.1007/BF01359909
  • László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673
  • E. Hewitt and K. Ross, Abstract harmonic analysis, Vol. 1, Academic Press, New York, 1963.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 96 (1986), 502-504
  • MSC: Primary 22A05
  • DOI:
  • MathSciNet review: 822449