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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
2. Kaul, S.K., on pointwise periodic transformation groups, Proc. Amer. Math. Soc. Vol. 27 (1971), pp. 391-394.Google Scholar
3. Montgomery, D., Pointwise periodic homeomorphisms, American J. Math. Vol. 59 (1937), pp. 118-120.Google Scholar
4. Montgomery, D. and Zippin, L., Topological transformation groups, Interscience Publication, Inc. N.Y. 1955.Google Scholar
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