On Some Chaos Notions of Supra Topological Space

In this paper, we investigate the dynamics of supra topological space. We introduce some concepts of supra chaos notions, i.e., supra transitive, supra minimal, supra totally transitive, supra mixing, supra locally everywhere onto (briefly, supra l.e.o), and supra weakly blending. First, we investigate some properties of supra transitive map, after that we figure out the relations of the supra chaos notions with the classical chaos notions and showed that supra l.e.o, supra mixing, supra totally transitive, and supra weakly blending implies l.e.o, topologically mixing, totally transitive, and weakly blending, respectively. Finally, we study the implication relations among the considered supra chaos notions and proved that supra l.e.o implies supra mixing, supra totally transitive, and supra weakly blending.