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

• Autorzy: Lorenz Halbeisen
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54E52: Baire category, Baire spaces
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2001
• Tom: 89
• Numer: 1
• Strony: 133-134

Daty

wydano

2001

Twórcy

autor

Lorenz Halbeisen

• Department of Pure Mathematics, Queen's University Belfast, Belfast BT7 1NN, Northern Ireland

Identyfikatory

DOI

10.4064/cm89-1-9