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20132026
most citedBornologies and filters in selection principles on function spaces

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math.LO2026

Existence of bases implies the axiom of choice, a foundation-free proof

Gabriel Fernandes, Renan Maneli Mezabarba, Vinicius de Oliveira Rodrigues

We prove that, in Zermelo--Fraenkel set theory with the axiom of Foundation removed, the statement that every vector space has a basis implies the Axiom of Choice (),…