Recurrence and almost periodicity in a generative transformation group
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- by Fred A. Roberson PDF
- Proc. Amer. Math. Soc. 32 (1972), 596-598 Request permission
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
- Walter Helbig Gottschalk and Gustav Arnold Hedlund, Topological dynamics, American Mathematical Society Colloquium Publications, Vol. 36, American Mathematical Society, Providence, R.I., 1955. MR 0074810
Additional Information
- © Copyright 1972 American Mathematical Society
- 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