LINEAR EXTENDERS AND THE AXIOM OF CHOICE - Université de La Réunion
Pré-Publication, Document De Travail Année : 2019

LINEAR EXTENDERS AND THE AXIOM OF CHOICE

Résumé

In set theory without the axiom of Choice ZF, we prove that for every commutative eld K, the following statement D_K : On every non nul K-vector space, there exists a non null linear form implies the existence of a K-linear extender on every vector subspace of a K-vector space. This solves a question raised in [9]. In the second part of the paper, we generalize our results in the case of spherically complete ultrametric valued elds, and show that Ingleton's statement is equivalent to the existence of continuous linear extenders.
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Dates et versions

hal-01478241 , version 1 (28-02-2017)
hal-01478241 , version 2 (16-01-2019)

Identifiants

  • HAL Id : hal-01478241 , version 2

Citer

Marianne Morillon. LINEAR EXTENDERS AND THE AXIOM OF CHOICE. 2019. ⟨hal-01478241v2⟩
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