Lyapunov Functions Of Attractors In Perfect-normal Hausdorff Spaces

This paper is concerned with converse Lyapunov theorems of attractors in Perfect-normal Hausdorff spaces.Firstly, from the view of admissible theory, we research the existence of attrac-tors of topological dynamical systems. Then we introduce the Lyapunov function of attractors in topological spaces. Finally, we proved the existence and construc-tion of Lyapunov functions of attractors in Perfect-normal Hausdorff spaces.