THE HAHN-BANACH THEOREM AND THE SEPARATION THEOREM IN A PARTIALLY ORDERED VECTOR SPACE - Kawasaki, T.; Toyoda, M.; Watanabe, T. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2011)
In this paper, using the Bourbaki-Kneser fixed point theorem, we give a new proof of the Hahn-Banach theorem in a partially ordered vector space and the separation theorem in the Cartesian product of a vector space and a partially ordered vector space.