Large convex sets in oriented matroids (Q1086574)

After a brief discussion of the axiom systems for oriented matroids we consider two basic types of convex sets, arising from the opposition, and establish some fundamental properties. These are used to investigate large convex sets, those containing at least one element from each opposite pair. A characterization is given for large convex sets, three types are examined, and the relationships between these three types are shown. These relationships are particularly strong in a dense space.