
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 deltaneighborhoods of convex sets; Relations with subsets of a kplane 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 ncells and (n1)pieces.
Descriptors : (*GEOMETRY, ALGEBRAIC TOPOLOGY), (*FUNCTIONAL ANALYSIS, SET THEORY), FUNCTIONS(MATHEMATICS), CONVEX SETS, THEOREMS
Distribution Statement : APPROVED FOR PUBLIC RELEASE