Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지

DYNAMICAL STABILITY AND SHADOWING PROPERTY OF CONTINUOUS MAPS

  • Koo, Ki-Shik (Department of Mathematics Taejon University) ;
  • Ryu, Hyun Sook (Department of Mathematics Chungnam National University)
  • Received : 1998.06.25
  • Published : 1998.07.31
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Abstract

This paper deals with the topological stability of continuous maps. First, the notion of local expansion is given and we show that local expansions of compact metric spaces have the shadowing property. Also, we prove that if a continuous surjective map f is a local homeomorphism and local expansion, then f is topologically stable in the class of continuous surjective maps. Finally, we find homeomorphisms which are not topologically stable.

Keywords

Acknowledgement

Supported by : Korea Science and Engineering Foundation