Accession Number : AD0619976

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

Corporate Author : ILLINOIS UNIV URBANA

Personal Author(s) : Cairns,Steward S.

Report Date : MAR 1963

Pagination or Media Count : 47

Abstract : Contents: Admissible neighborhoods of a polyhedron; Surrounding manifolds and delta-neighborhoods of convex sets; Relations with subsets of a k-plane in E(n); Polyhedral cells; The sets gamma (c): definition and basic properties; Supporting planes of a c(n); 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.

Descriptors :   (*GEOMETRY, ALGEBRAIC TOPOLOGY), (*FUNCTIONAL ANALYSIS, SET THEORY), FUNCTIONS(MATHEMATICS), CONVEX SETS, THEOREMS

Distribution Statement : APPROVED FOR PUBLIC RELEASE