On the complexity of Hamel bases of infinite dimensional Banach spaces

2001/09/23 by Lorenz Halbeisen
Mathematics · #math.LO #msc:46B20 #msc:54E52

paper · pdf

published as Colloquium Mathematicum 89 (2001) 133-134

arxiv created 2001/09/23 · arxiv updated 2009/11/30

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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