  Properties of Lipschitz and d.c. surfaces of finite codimension in a Banach
space, and properties of generated $\sigma$-ideals are studied. These
$\sigma$-ideals naturally appear in the differentiation theory and in the
abstract approximation theory. Using these properties, we improve an
unpublished result of M. Heisler which gives an alternative proof of a result
of D. Preiss on singular points of convex functions.
