Intersections of continuous, Lipschitz, Hölder class, and smooth functions

Abstract

We present some improvements of known theorems and examples concerning intersections of continuous or Lipschitz functions with smooth functions or intersections of smooth functions or Hölder class functions with smoother functions. We are particularly concerned with our ability to 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).