Geodesic
On the complexity of Hamel bases of infinite-dimensional Banach spaces
Lorenz Halbeisen1
1 Department of Pure Mathematics Queen's University Belfast Belfast BT7 1NN, Northern Ireland
Colloquium Mathematicum, Tome 89 (2001) no. 1, pp. 133-134 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 is shown that a Hamel basis of an infinite-dimensional Banach space can never be linearly Borel. This answers a question of Anatoliĭ Plichko.
DOI : 10.4064/cm89-1-9
Keywords: call subset topological vector space linearly borel every finite number set linear combinations length borel subset shown hamel basis infinite dimensional banach space never linearly borel answers question anatoli plichko

Lorenz Halbeisen 1

1 Department of Pure Mathematics Queen's University Belfast Belfast BT7 1NN, Northern Ireland 
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Lorenz Halbeisen. On the complexity of Hamel bases
of infinite-dimensional Banach spaces. Colloquium Mathematicum, Tome 89 (2001) no. 1, pp. 133-134. doi: 10.4064/cm89-1-9

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