On the complexity of Hamel bases of infinite dimensional Banach spaces
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borelbanachdimensionalhamelinfinitelinearlyspacesubset
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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.
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