THE HAHN-BANACH THEOREM AND THE SEPARATION THEOREM IN A PARTIALLY ORDERED VECTOR SPACE

TOSHIHARU  KAWASAKI; MASASHI  TOYODA; TOSHIKAZU  WATANABE

THE HAHN-BANACH THEOREM AND THE SEPARATION THEOREM IN A PARTIALLY ORDERED VECTOR SPACE

Authors

TOSHIHARU KAWASAKI College of Engineering, Nihon University, 1 Nakagawara, Tokusada, Tamuramachi, Koriyamashi, Fukushima 963-8642, Japan
MASASHI TOYODA Faculty of Engineering, Tamagawa University, 6-1-1 Tamagawagakuen, Machidashi, Tokyo 194-8610, Japan
TOSHIKAZU WATANABE Graduate School of Science and Technology, Niigata University, 8050, Igarashi 2-no-cho, Nishiku, Niigata, 950-2181, Japan

Keywords:

Fixed point theorem, Hahn-Banach theorem, Separation theorem, Partially ordered vector space

Abstract

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.