On the complexity of Hamel bases of infinite dimensional Banach spaces
Logic
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0109177,
title = {On the complexity of Hamel bases of infinite dimensional Banach spaces},
author = {Lorenz Halbeisen},
journal= {arXiv preprint arXiv:math/0109177},
year = {2007}
}