On the complexity of Hamel bases of infinite-dimensional Banach spaces
Colloquium Mathematicae (2001)
- Volume: 89, Issue: 1, page 133-134
- ISSN: 0010-1354
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topLorenz Halbeisen. "On the complexity of Hamel bases of infinite-dimensional Banach spaces." Colloquium Mathematicae 89.1 (2001): 133-134. <http://eudml.org/doc/284056>.
@article{LorenzHalbeisen2001,
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.},
author = {Lorenz Halbeisen},
journal = {Colloquium Mathematicae},
keywords = {Baire property; Banach space; Borel set; Hamel basis; Baire category},
language = {eng},
number = {1},
pages = {133-134},
title = {On the complexity of Hamel bases of infinite-dimensional Banach spaces},
url = {http://eudml.org/doc/284056},
volume = {89},
year = {2001},
}
TY - JOUR
AU - Lorenz Halbeisen
TI - On the complexity of Hamel bases of infinite-dimensional Banach spaces
JO - Colloquium Mathematicae
PY - 2001
VL - 89
IS - 1
SP - 133
EP - 134
AB - 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.
LA - eng
KW - Baire property; Banach space; Borel set; Hamel basis; Baire category
UR - http://eudml.org/doc/284056
ER -
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