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.
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