Is "Every vector space admits a norm" weaker than AC? I know that the statement follows from "Every vector space has a basis", which is equivalent to AC.
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Of course only real/complex vector spaces are of interest here. – Damian Reding Mar 13 '15 at 08:47
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http://math.stackexchange.com/questions/326653/do-you-need-the-axiom-of-choice-to-assert-that-every-real-vector-space-has-a-nor is related. – Asaf Karagila Mar 15 '15 at 13:47