arXiv math/01091772001-09-23math.LO

On the complexity of Hamel bases of infinite dimensional Banach spaces

Lorenz Halbeisen

发表信息：: Colloquium Mathematicum 89 (2001) 133-134

英文摘要：

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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