There are no stable points for continuum-wise expansive homeomorphisms
  We obtain some results about continuum-wise expansive homeomorphisms, such as non-existence of stable points and presence of non-trivial connected components within the local stable and unstable sets. These facts have been of importance in theorems of classification of expansive homeomorphisms. They are achieved now, however, by new and self contained techniques that hold on more general settings. 
Jana Rodriguez Hertz