ON THE COUNTABLE COMPACTA AND EXPANSIVE HOMEOMORPHISMS

  • Kim, In-Su (Department of Mathematics, Chonbuk National University) ;
  • Kato, Hisao (Institute of mathematics, university of Tsukuba) ;
  • Park, Jong-Jin (Department of Mathematics, Chonbuk National University)
  • Published : 1999.05.01

Abstract

In this paper we introduce the notions of expansive homeomorphism and its properties, and study the relation between countable compacta and ordinal numbers. Our results extend and improve those of T.Kimura and others.

References

  1. Colloq.Math. v.49 The spliting of zero-dimensional automorphisms and its application N. Aoki
  2. Vanderbit University,Thesis Unstable self-homeomorphisms of a compact space B. F. Bryant
  3. Tokyo J. Math. v.6 Homeomorphisms with the pseudo orbit tracing property of the cantor set M. Dateyama
  4. There are no expansive homeomorphisms on $S^2$,Preprint K. Hiraide
  5. Pacific J. Math. v.10 The nonexistence of expansive homeomorphisms on a closed 2-cell J. F. Jakobsen;W. R. utz
  6. Tsukuba. J. Math. v.12 Homeomorphisms of zero-dimensional spaces T. Kimura
  7. Topology v.1 K. Kuratowski
  8. Trans. Amer. Math. Soc. v.252 Expansive homeomorphisms and topological dimension R. Mane
  9. Continuum Theory: An Introduction S. B. Nadler, Jr.
  10. Math. Systems theory v.6 Expansive self-homeomorphisms of the Cantor set M. Sears
  11. Proc. Amer. Math. Soc. v.1 Unstable homeomorphisms W. R. Utz