Original Articles

UNIFORM SMOOTHNESS ENTAILS HAHN-BANACH

Published in: Quaestiones Mathematicae
Volume 24 , issue 4, pages: 425–439
DOI: 10.1080/16073606.2001.9639231
Author(s): Edmond AlbiusERMIT, Département de Mathématiques et Informatique, France, Marianne MorillonERMIT, 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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