On pointwise periodic transformation groups
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- by S. K. Kaul
- Proc. Amer. Math. Soc. 27 (1971), 391-394
- DOI: https://doi.org/10.1090/S0002-9939-1971-0267551-6
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Abstract:
Let $X$ be a connected and metrizable manifold without boundary, and $(X,T)$ a transformation group. We prove that if $T$ is countable and pointwise periodic then $T$ is periodic. This is a generalization of a result of Montgomery, which says that if $h$ is a pointwise periodic homeomorphism of $X$ onto itself then $h$ is 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
- Deane Montgomery, Pointwise Periodic Homeomorphisms, Amer. J. Math. 59 (1937), no. 1, 118–120. MR 1507223, DOI 10.2307/2371565 M. H. A. Newman, A theorem on periodic transformations of spaces, Quart. J. Math. 2 (1931), 1-8.
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 391-394
- MSC: Primary 54.80
- DOI: https://doi.org/10.1090/S0002-9939-1971-0267551-6
- MathSciNet review: 0267551