  In this article we characterize monotone extensions of cw-expansive
homeomorphisms of compact metric spaces. We study the topology of its quotient
space in the case of a compact surface. These results are applied to prove that
there are cw-expansive homeomorphisms of compact surfaces with infinitely many
fixed points and empty wandering set. The examples are quotients of topological
perturbations of pseudo-Anosov diffeomorphisms. We also show that there is a
cw-expansive homeomorphism with the shadowing property of the 2-sphere.
