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Etats, idéaux et axiomes de choix

Abstract : We work in ZF, set theory without Axiom of Choice. Using weak forms of Axiom of Choice, for example Hahn-Banach axiom HB : "Every linear form on a vector subspaceof a vector space E, increased by a sublinear form p can be extended to a linear form on E increased by p", or Tychonov axiom T2 : "Every product of compact Haussdorf is compact, we study the existence of states on ordered groups with order unit. We continue giving links between left ideals and states on C*-algebras.
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Submitted on : Thursday, February 8, 2018 - 3:08:07 PM
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Martine Barret. Etats, idéaux et axiomes de choix. Mathématiques générales [math.GM]. Université de la Réunion, 2017. Français. ⟨NNT : 2017LARE0025⟩. ⟨tel-01704523⟩

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