Uniform Smoothness Entails Hahn-Banach
AbstractWe 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