Expansive homeomorphisms with the shadowing property on zerodimensional spaces

Abstract

Let X = fag [ fai j i 2 Ng be a subspace of Euclidean space E2 such that limi!1 ai = a and ai 6= aj for i 6= j. 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 = fa; bg [ fai j i 2 Zg is a subspace of E2 such that limi!1 ai = b and limi!¡1 ai = a with the following properties; ai 6= aj for i 6= j and a 6= b.