INTERSECTION THEOREMS FOR POSITIVE SETS

Abstract

In a vector space over an ordered field, a positive set is one that is closed under the operation of forming linear combinations with nonnegative coefficients; it may be described alternatively as a convex cone whose apex is the origin. Such sets arise naturally as solutions of systems of homogeneous linear inequalities, and the intersection theorems proved here can be reformulated as consistency theorems for such systems. The main tool used in proving the intersection theorems is a characterization and classification of sets which enjoy a strong independence property with respect to the formation of nonnegative linear combinations.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1969
Accession Number
AD0683773

Entities

People

  • Victor Klee
  • Wolfhard Hansen

Organizations

  • Boeing

Tags

DTIC Thesaurus Topics

  • Algebra
  • Convex Sets
  • Functions (Mathematics)
  • Inequalities
  • Linear Algebra
  • Mathematical Analysis
  • Mathematics
  • Military Research
  • Scalar Functions
  • Sequences
  • Set Theory
  • Theorems
  • Universities
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Aerodynamics/Aeronautics.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space