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

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.

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1963
Accession Number
AD0619976

Entities

People

  • Steward S. Cairns

Organizations

  • University of Illinois Urbana–Champaign

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Additives (Chemicals)
  • Convex Sets
  • Mathematical Analysis
  • Mathematics
  • Theorems

Readers

  • Approximation Theory.
  • Internal Combustion Engine (ICE) Technology.
  • Operations Research