Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Extension of a theorem of Baayen and Helmberg on monothetic groups
HTML articles powered by AMS MathViewer

by D. L. Armacost PDF
Proc. Amer. Math. Soc. 96 (1986), 502-504 Request permission

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 $K$.
References
  • D. L. Armacost, Remark on my paper: “Generators of monothetic groups”, Canadian J. Math. 25 (1973), 672. MR 316623, DOI 10.4153/CJM-1973-067-5
  • David L. Armacost, The structure of locally compact abelian groups, Monographs and Textbooks in Pure and Applied Mathematics, vol. 68, Marcel Dekker, Inc., New York, 1981. MR 637201
  • 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.
  • L. Kuipers and H. Niederreiter, Uniform distribution of sequences, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. MR 0419394
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 22A05
  • Retrieve articles in all journals with MSC: 22A05
Additional Information
  • © 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