abstract
##

On the complexity of Hamel bases of infinite dimensional Banach
spaces

Lorenz Halbeisen

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We call a subset *S* of a topological vector space *V* linearly
Borel, if for every finite number *n*, the set of all linear
combinations of *S* of length *n* is a Borel subset of *V*. It will
be shown that a Hamel base of an infinite dimensional Banach space
can never be linearly Borel. This answers a question of Anatolij
Plichko.