A note on transitivity in set-valued discrete systems

Let (X,d) be a metric space and f:X→X is a continuous function. If we consider the space of all non-empty compact subsets of X endowed with the Hausdorff metric induced by d and , , then the aim of this work is to show that f̄ transitive implies f transitive. Also, we give an example showing that f transitive does not implies f̄ transitive.