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Sequential compactness and the axiom of choice.

Sequential compactness and the axiom of choice.

A theorem is effective iff it is proved in ZF°, where ZF° is ZermeloFraenkel set theory without the axioms of choice and foundation (regularity). A well known effective theorem of F. Riesz states that a Hubert space is finite dimensional iff its closed unit ball is compact. This may fail …