Ingleton's theorem and the Axiom of Choice

Marianne Morillon (1)

1 LIM - Laboratoire d'Informatique et de Mathématiques

Ingleton's theorem, a p-adic analog of Hahn-Banach's theorem, states that given a spherically complete ultrametric valued field K, and an ultrametric semi-norm p on a K-vector space E, any linear form f defined on a vector subspace V of E such that |f|≤ p can be extended into a linear form f̃ which is defined on E and such that |f̃| ≤ p. In his paper "The Axiom of Choice in p-adic functional analysis" (Lecture Notes in Pure and Appl. Math., 137, Dekker, New York, 1992), A.C.M. van Rooij studied Ingleton's statement in set-theory without the Axiom of Choice and asked several questions. We propose some additional results to this topic.

Keywords: Axiom of Choice; Ultrametric Hahn-Banach

Domains: Mathematics [math]

Marianne Morillon. Ingleton's theorem and the Axiom of Choice. 33rd Summer Conference on Topology and its Applications, Western Kentucky University Bowling Green, Kentucky, USA, Jul 2018, Bowling Green (Kentucky), United States. ⟨hal-04553635⟩