Original Articles

UNIFORM SMOOTHNESS ENTAILS HAHN-BANACH

Published in: Quaestiones Mathematicae
Volume 24 , issue 4 , 2001 , pages: 425–439

DOI: 10.1080/16073606.2001.9639231

Author(s): Edmond Albius ERMIT, Département de Mathématiques et Informatique, France , Marianne Morillon ERMIT, Département de Mathématiques et Informatique, France

Keywords: Primary 03E25 , Secondary 46 , Primary 03E25 , Secondary 46

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Abstract

We show in set theory ZF (without the Axiom of Choice), that uniformly smooth normed spaces satisfy an effective and geometric form of the Hahn-Banach property. We also compare in ZF the two notions of Gâteaux differentiability and smoothness of a norm, and we obtain a new equivalent of the Hahn-Banach axiom.

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