Uniform Smoothness Entails Hahn-Banach

  • Edmond Albius ERMIT, Département de Mathématiques et Informatique, Université de La Réunion, 15 avenue René Cassin - BP 7151 - 97715 Saint-Denis Messag. Cedex 9 France.
  • Marianne Morillon ERMIT, Département de Mathématiques et Informatique, Université de La Réunion, 15 avenue René Cassin - BP 7151 - 97715 Saint-Denis Messag. Cedex 9 France.

Abstract

We in Zermelo-Fraenkel set theory ZF (without the Axiom of Choice), and we denote by ZFC set theory with the Axiom of Choice. Our paper deals with the role of the Axiom of Choice in functional analysis, and more particularly, with the necessity of using the Axiom of Choice when invoking some consequence of the following Hahn-Banach axiom HB.
Mathematics Subject Classification (2000): Primary 03E25; Secondary 46.
Keywords: axiom of choice, banach space, Hahn-Banach, uniformly smooth, ZF, functional analysis, Zermelo-Fraenkel, Mazur property, ZFC, HB, Gâteaux differentiability, Fréchet differentiability, q-Engel series, John Knopfmacher, partition, identities, study, Santos polynomials, polynomials

Quaestiones Mathematicaes 24 (4) 2001, 425–439
Published
2004-03-15
Section
Articles

Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606