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Recurrence and almost periodicity in a generative transformation group


Author: Fred A. Roberson
Journal: Proc. Amer. Math. Soc. 32 (1972), 596-598
MSC: Primary 54H15
DOI: https://doi.org/10.1090/S0002-9939-1972-0293609-2
MathSciNet review: 0293609
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Abstract: A point p in a transformation group (X, T, II) is recurrent if for every neighborhood U of p there is an extensive set $ E \subset T$ such that $ pE \subset U$. The point p is almost periodic if there is a syndetic set $ A \subset T$ such that $ pA \subset U$. This paper proves that a recurrent point in a locally compact, generative transformation group with an equicontinuous neighborhood must also be almost periodic.


References [Enhancements On Off] (What's this?)

  • [1] W. H. Gottschalk and G. A. Hedlund, Topological dynamics, Amer. Math. Soc. Colloq. Publ., vol. 36, Amer. Math. Soc., Providence, R.I., 1955. MR 17, 650. MR 0074810 (17:650e)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0293609-2
Keywords: Transformation group, generative, recurrent, almost periodic, equicontinuous
Article copyright: © Copyright 1972 American Mathematical Society

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