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

Tom 89 / 2001

Lorenz Halbeisen Colloquium Mathematicum 89 (2001), 133-134 MSC: Primary 46B20; Secondary 54E52. DOI: 10.4064/cm89-1-9

Streszczenie

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.

Autorzy

  • Lorenz HalbeisenDepartment of Pure Mathematics
    Queen's University Belfast
    Belfast BT7 1NN, Northern Ireland
    e-mail

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