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We show that in set-theory without the axiom of choice ZF, the statement sH: Every proper closed subset of a nitary matroid is the intersection of hyperplanes including it implies AC fin , the axiom of choice for (nonemp...
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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-lin...
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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 Johnson (1977) : "If a normed space $E$ does n...