Uniform Smoothness Entails Hahn-banach

  title={Uniform Smoothness Entails Hahn-banach},
  author={EDMOND ALBIUS and Marianne Morillon},
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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