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Pointwise Finite Families of Mappings

Published online by Cambridge University Press:  20 November 2018

James W. Roberts
James W. Roberts*
Affiliation:
University of South Carolina
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In [3], Montgomery proved that if h is a pointwise periodic homeomorphism of a connected manifold without boundary onto itself, then h is periodic. Kaul generalized this result in [2] by showing that if X is a connected metrizable manifold without boundary and if (X, T)is a transformation group with T countable such that T is pointwise periodic, then T is periodic.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 5 , 01 December 1975 , pp. 767 - 768
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Gottschalk, W.E. and Hedlund, G.A., Topological dynamics, Amer. Math. Soc. Colloq. Publ. Vol. 36, 1955.Google Scholar
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3. Montgomery, D., Pointwise periodic homeomorphisms, American J. Math. Vol. 59 (1937), pp. 118-120.Google Scholar
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5. Smith, P.A., Transformations of finite period, III, Newman's theorem, Ann. of Math. Vol. 42 (1941), pp. 446-458.Google Scholar
6. Yang, J.S., On pointwise periodic transformation groups, Notices Amer. Math. Soc. Vol. 18 (1971), p. 830 (71T-G125).Google Scholar