On pointwise periodic transformation groups
Abstract: Let be a connected and metrizable manifold without boundary, and a transformation group. We prove that if is countable and pointwise periodic then is periodic. This is a generalization of a result of Montgomery, which says that if is a pointwise periodic homeomorphism of onto itself then is periodic.
-  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, https://doi.org/10.2307/2371565
-  M. H. A. Newman, A theorem on periodic transformations of spaces, Quart. J. Math. 2 (1931), 1-8.
- W. E. 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)
- D. Montgomery, Pointwise periodic homeomorphisms, Amer. J. Math. 59 (1937), 118-120. MR 1507223
- M. H. A. Newman, A theorem on periodic transformations of spaces, Quart. J. Math. 2 (1931), 1-8.
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Keywords: Transformation group, manifold, pointwise periodic, periodic, equicontinuous, lower semicontinuous
Article copyright: © Copyright 1971 American Mathematical Society