abstract
On the complexity of Hamel bases of infinite dimensional Banach
spaces
Lorenz Halbeisen
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.