| Abstract: |
| In this talk, we introduce the notions of symbolic expansivity and symbolic shadowing for homeomorphisms on non-metrizable spaces which are generalizations of expansivity and shadowing for metric spaces, respectively. The main result is to generalize the Smales spectral decomposition theorem to symbolically expansive homeomorphisms with symbolic shadowing on non-metrizable compact Hausdorff totally disconnected spaces. Furthermore, we consider the topological stability for homeomorphisms on the spaces. |
|