Abstract: Let (X,d) be a compact metric space and f : X→X a continuous mapping, then (k(X),H) is d induced Hausdorf f metric space of all non-empty comp act subsets of X and f: k(X)→k(X), f(A)={f(a)|a∈A}. We invest igated the relationships between the chaotici ty of some set-valued discrete dynamical systems associated with f , the weakly topologically mixing and the topologically mixing of f with the chaoticity of f.

Key words: chaos, topological mixing, weakly topologically mixing