INTERSECTIONS OF CONTINUOUS, LIPSCHITZ, HOLDER CLASS, AND SMOOTH FUNCTIONS

We present some improvements of known theorems and examples concerning intersections of continuous or Lipschitz functions with smooth functi ons or intersections of smooth functions or Holder class functions wit h smoother functions. We are particularly concerned with our ability t o force the projection of the intersection to be uncountable within a given set M which is either large in measure or in category (or both).