Ordered Incidence Geometry and the Geometric Foundations of Convexity Theory.

Abstract

An Ordered Incidence Geometry, that is a geometry with certain axioms of incidence and order is proposed as a minimal setting for the fundamental convexity theorems, such as the hyperplane separation theorem and the theorems of Radon and Helly. These theorems are usually stated, proved, understood and/or applied in the context of a linear vector space, but they require only incidence and order, (and for separation, completeness), and none of the linear structure of a vector space.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1984
Accession Number
ADA144286

Entities

People

  • A. Ben-israel
  • A. Ben-tal

Organizations

  • University of Texas at Austin

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Algebra
  • Contracts
  • Convex Sets
  • Geometry
  • Intervals
  • Monotone Functions
  • New York
  • Plane Geometry
  • Security
  • Standards
  • Theorems
  • Three Dimensional
  • Triangles
  • Two Dimensional
  • United States
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space