  We consider partially hyperbolic diffeomorphisms on compact manifolds where
the unstable and stable foliations stably carry some unique non-trivial
homologies. We prove the following two results: if the center foliation is one
dimensional, then the topological entropy is locally a constant; and if the
center foliation is two dimensional, then the topological entropy is continuous
on the set of all $C^\8$ diffeomorphisms. The proof uses a topological
invariant we introduced; Yomdin's theorem on upper semi-continuity; Katok's
theorem on lower semi-continuity for two dimensional systems and a refined
Pesin-Ruelle inequality we proved for partially hyperbolic diffeomorphisms.
