DIFFERENTIABLE APPROXIMATIONS AND THE SCHOENFLIES THEOREM FOR POLYHEDRA. PART I. NEIGHBORHOODS, SURROUNDING MANIFOLDS, SMOOTHING FUNCTIONS,

Contents Admissible neighborhoods of a polyhedron Surrounding manifolds and delta-neighborhoods of convex sets Relations with subsets of a k-plane in En Polyhedral cells The sets gamma c definition and basic properties Supporting planes of a cn Analysis of the sets gamma c Definition of surgery C infinity approximations to piecewise linear functions Additive smoothing functions Manifolds of class D infinity Neighborhoods and surrounding manifolds, a recurrent procedure and Formulas for the n-cells and n-1-pieces.