Intersection Theorems for Positive Sets

摘要

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. (Author)