  We give a definition of chaos for a continuous self-map of a general
topological space. This definition coincides with the Devanney definition for
chaos when the topological space happens to be a metric space. We show that in
a uniform Hausdorff space, there is a meaningful definition of sensitive
dependence on initial conditions, and prove that if a map is chaotic on a such
a space, then it necessarily has sensitive dependence on initial conditions.
The proof is interesting in that it explains very clearly what causes a chaotic
process to have sensitive dependence. Finally, we construct a chaotic map on a
non-metrizable topological space.
