학술저널
DYNAMICAL STABILITY AND SHADOWING PROPERTY OF CONTINUOUS MAPS
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 11, No. 1
-
1998.0873 - 85 (13 pages)
- 3
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.
Abstract
1. Introduction and Preliminaries
2. Local expansions
3. Topologically stable maps
4. Homeomorphisms which are not topologically stable
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