Uniform Eberlein Spaces and the Finite Axiom of Choice
نویسنده
چکیده
We work in set-theory without choice ZF. Given a closed subset F of [0, 1] which is a bounded subset of l(I) (resp. such that F ⊆ l(I)), we show that the countable axiom of choice for finite subsets of I, (resp. the countable axiom of choiceACN) implies that F is compact. This enhances previous results where ACN (resp. the axiom of Dependent Choices DC) was required. Moreover, if I is linearly orderable (for example I = R), the closed unit ball of l(I) is weakly compact (in ZF).
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