Periodica Mathematica Hungarica

, Volume 31, Issue 2, pp 123–130 | Cite as

Expansive self-homeomorphisms on G-spaces

  • Ruchi Das
Article

Abstract

Beginning with examples, the notion ofG-expansiveness over a metric spaceX on which a topological groupG acts is introduced. Some conditions are determined under which expansiveness onX impliesG-expansiveness. A characterization of aG-expansive homeomorphism is obtained which in turn gives a sufficient condition for the homeomorphic extension of aG-expansive homeomorphism to beG-expansive. At the end, some results are stated in the form of concluding remarks.

Mathematics subject classification numbers

1991. Primary 54C10 Secondary 54H20 

Key words and phrases

G-spaces expansive homeomorphisms 

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References

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    Bredon, G. E.,Introduction to compact transformation groups, Academic Press, New York and London, 1972.Google Scholar
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    Bryant, B. F., Expansive self-homeomorphisms of a compact metric space,Amer. Math. Monthly,69 (1962), 386–391.Google Scholar
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    Utz, W. R., Unstable homeomorphisms,Proc. Amer. Math. Soc.,1 (1950), 769–774.Google Scholar
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    Walters, P.,An introduction to ergodic theory, Springer-Verlag, New York Inc., 1982.Google Scholar
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    Wine, J. D., Extending expansive homeomorphisms,Proc. Amer. Math. Soc.,86 (1982), 531–534.Google Scholar

Copyright information

© Akadémiai Kiadó 1995

Authors and Affiliations

  • Ruchi Das
    • 1
  1. 1.Department of Mathematics Faculty of ScienceThe M. S. University of BorodaVadodaraIndia

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