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On the complexity of Hamel bases of infinite dimensional Banach spaces

Lorenz Halbeisen
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Abstract

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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BibTeXRIS

Lorenz Halbeisen. 2001-09-23. On the complexity of Hamel bases of infinite dimensional Banach spaces. https://arxiv.org/abs/math/0109177

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