What is the cardinality of a Hamel basis of $\ell_1(\mathbb R)$? Is it deducible in ZFC that it is seemingly continuum? Does it follow from this that each Banach space of density $\leqslant 2^{\aleph_0}$ has a Hamel basis of cardinality continuum (OK, I do know it cannot be smaller for an inf.-dim. Banach space)?
Cardinality of a Hamel basis of $\ell_1(\mathbb{R})$
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functional-analysis
set-theory
vector-spaces
banach-spaces
cardinals
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0See also [this question](http://math.stackexchange.com/q/427834/462). – 2013-06-24