SHIFTLIKE APPROXIMATIONS AND TOPOLOGICAL MIXING

Abstract

We show that every map in the group G of self-homeomorphisms of the bisequence space can be approximated by homeomorphisms which “look like” the shift map and are expansive. By removing a certain open set of maps from G, we obtain a closed subspace M which contains all mixing maps. If φ · M then any shiftlike approximation to φ is topologically strong mixing. Thus the strong mixing expansive maps are dense in M. Further the weak mixing maps form a dense Gδ sets in M.