On the complexity of Hamel bases of infinite-dimensional Banach spaces
Volume 89 / 2001
Colloquium Mathematicum 89 (2001), 133-134
MSC: Primary 46B20; Secondary 54E52.
DOI: 10.4064/cm89-1-9
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 is shown that a Hamel basis of an infinite-dimensional Banach space can never be linearly Borel. This answers a question of Anatoliĭ Plichko.
