5 papers
Linear extenders and the Axiom of Choice
Marianne Morillon
In set theory without the axiom of Choice ZF, we prove that for every commutative field IK, the following statement D_{\IK}: "On every non null IK-vector space, there exists a non…
Multiple Choices imply the Ingleton and Krein-Milman axioms
Marianne Morillon
In set theory without the Axiom of Choice, we consider Ingleton's axiom which is the counterpart in ultrametric analysis of the Hahn-Banach axiom. We show that in , set theory…
Uniform Eberlein spaces and the finite axiom of choice
Marianne Morillon
We work in set-theory without choice $\ZF$. Given a closed subset of which is a bounded subset of ({\em resp.} such that ), we show…
Countable Choice and Compactness
Marianne Morillon
We work in set-theory without choice ZF. Denoting by AC(N) the countable axiom of choice, we show in ZF+AC(N) that the closed unit ball of a uniformly convex Banach space is compac…
A new proof of James' sup theorem
Marianne Morillon
We provide a new proof of James' sup theorem for (non necessarily separable) Banach spaces. One of the ingredients is the following generalization of a theorem of Hagler and Johnso…