Topological Structure of Non–wandering Set of a Graph Map.

Let G be a graph (i.e., a finite one–dimensional polyhedron) and f : G → G be a continuous map. In this paper, we show that every isolated recurrent point of f is an isolated non–wandering point; every accumulation point of the set of non–wandering points of f with infinite orbit is a two–order accumulation point of the set of recurrent points of f; the derived set of an ω–limit set of f is equal to the derived set of an the set of recurrent points of f; and the two–order derived set of non–wandering set of f is equal to the two–order derived set of the set of recurrent points of f. [ABSTRACT FROM AUTHOR]