Answer by Asaf Karagila for Characterizing Vector Spaces without (provable)...
To my knowledge there is no such condition. Certainly not at the generality you're asking for.The closest we can get is "infinite dimensional Banach space" (well, to be honest we can go quite a lot...
View ArticleCharacterizing Vector Spaces without (provable) Basis in ZF
Without the axiom of choice certain vector spaces cannot be proven to have a (hamel) basis in ZF alone and I am wondering whether there exists some criteria characterizing such spaces.Here is what I...
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