EXPANSIVE HOMEOMORPHISMS WITH THE SHADOWING PROPERTY ON ZERO DIMENSIONAL SPACES

- Journal title : Communications of the Korean Mathematical Society
- Volume 19, Issue 4, 2004, pp.759-764
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2004.19.4.759

Title & Authors

EXPANSIVE HOMEOMORPHISMS WITH THE SHADOWING PROPERTY ON ZERO DIMENSIONAL SPACES

Park, Jong-Jin;

Park, Jong-Jin;

Abstract

Let X = {a} { ${}$i N} be a subspace of Euclidean space such that = a and for . Then it is well known that the space X has no expansive homeomorphisms with the shadowing property. In this paper we show that the set of all expansive homeomorphisms with the shadowing property on the space Y is dense in the space H(Y) of all homeomorphisms on Y, where Y = {a, b} {$a_{i}{}i{\in}Z$} is a subspace of such that - = b and = a with the following properties; for and .

Keywords

expansive homeomorphism;-pseudo-orbit;shadowing property (pseudo orbit tracing property);Dense;Zero dimensional space;

Language

English

Cited by

References

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