Devaney’s chaotic on induced maps of hyperspace

Let (X, d) be a metric space and let f : X → X   be a continuous map. In Section 2, the relationships among the chaoticity of f¯, f˜ and f are investigated while 2X, C(X) are taken We-topology. In Section 3, the relationships among the chaoticity of f¯, f˜, and f are investigated while X is a graph.