Separation theorems for oriented matroids

doi:10.1016/0012-365X(88)90006-4

Discrete Mathematics

Volume 70, Issue 3, August 1988, Pages 303-310

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Abstract

In this paper we show that Minty's lemma can be used to prove the Hahn-Banach theorem as well as other theorems in this class such as Radon's and Helly's theorem for oriented matroids having an intersection property which guarantees that every pair of flats intersects in some point extension $O$ ∪ p of the oriented matroid $O$ .

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^∗: Supported by the German Research Association (Deutsche Forschungsgemeinschaft, SFB 303).