CHAOS IN TOPOLOGICAL SPACES

We give a definition of chaos for a continuous self map of a general topological space. We show that in a uniform Hausdorff space there is a meaningful definition of sensitive dependence on initial conditions. We prove that a continuous self map of a uniform Hausdorff space that is chaotic in the sense defined is necessarily sensitively dependent on initial conditions. Finally, we exhibit a chaotic map on a non-metrizable topological space.