On the complexity of Hamel bases of infinite dimensional Banach spaces

Details On the complexity of Hamel bases of infinite dimensional Banach spaces On the complexity of Hamel bases of infinite dimensional Banach spaces

2001-09-23

arxiv.org/abs/math/0109177v1

Colloquium Mathematicum 89 (2001) 133-134

Mathematics

Logic

Scientific paper

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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