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Limited spaces

N. De Grande-De Kimpe, C. Perez-Garcia (1995)

Annales mathématiques Blaise Pascal

Linear extenders and the Axiom of Choice

Marianne Morillon (2017)

Commentationes Mathematicae Universitatis Carolinae

In set theory without the Axiom of Choice ZF, we prove that for every commutative field 𝕂 , the following statement 𝐃 𝕂 : “On every non null 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 Morillon M., Linear forms and axioms of choice, Comment. Math. Univ. Carolin. 50 (2009), no. 3, 421-431. In the second part of the paper, we generalize our results in the case of spherically...

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