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LINEAR EXTENDERS AND THE AXIOM OF CHOICE

Abstract : 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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https://hal.univ-reunion.fr/hal-01478241
Contributor : Marianne Morillon <>
Submitted on : Wednesday, January 16, 2019 - 8:19:35 AM
Last modification on : Monday, September 2, 2019 - 9:41:19 AM

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

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