  In this paper we study local stable/unstable sets of sensitive homeomorphisms
with the shadowing property defined on compact metric spaces. We prove that
local stable/unstable sets always contain a compact and perfect subset of the
space. As a corollary we generalize results in [6] and [11] proving that
positively countably expansive homeomorphisms defined on compact metric spaces
satisfying either transitivity and the shadowing property, or the L-shadowing
property, can only be defined in countably spaces.
