Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [12 references]  Display  Hide  Download

https://hal.univ-reunion.fr/hal-01478241
Contributor : Marianne Morillon <>
Submitted on : Tuesday, February 28, 2017 - 8:03:53 AM
Last modification on : Thursday, March 28, 2019 - 11:24:10 AM
Long-term archiving on: : Monday, May 29, 2017 - 12:50:36 PM

File

linear_extenders_hal.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01478241, version 1

Citation

Marianne Morillon. LINEAR EXTENDERS AND THE AXIOM OF CHOICE. 2017. ⟨hal-01478241v1⟩

Share

Metrics

Record views

112

Files downloads

35