Whitney, Thom, Mather, Arnold and others develoved the singularity theory of smooth maps. Does there exist any analogue of this theory in the category of TOP or PL (or Lipschitz) maps? I mean notions like: stability, hierarchy of singularities, nice dimensions, arising stratification on the source and on the target of a map, according to the germ type of the map at the points, Thom polynomials.