  We obtain an improved version of the area theorem for not necessarily
differentiable horizons which, in conjunction with a recent result on the
completeness of generators, allows us to prove that under the null energy
condition every compactly generated Cauchy horizon is smooth and compact. We
explore the consequences of this result for time machines, topology change,
black holes and cosmic censorship. For instance, it is shown that compact
Cauchy horizons cannot form in a non-empty spacetime which satisfies the stable
dominant energy condition wherever there is some source content.
