On countable families of sets without the Baire property

Mats Aigner, Vitalij A. Chatyrko, and Venuste Nyagahakwa. "On countable families of sets without the Baire property." Colloquium Mathematicae 133.2 (2013): 179-187. <http://eudml.org/doc/283890>.

@article{MatsAigner2013,
abstract = {We suggest a method of constructing decompositions of a topological space X having an open subset homeomorphic to the space (ℝⁿ,τ), where n is an integer ≥ 1 and τ is any admissible extension of the Euclidean topology of ℝⁿ (in particular, X can be a finite-dimensional separable metrizable manifold), into a countable family ℱ of sets (dense in X and zero-dimensional in the case of manifolds) such that the union of each non-empty proper subfamily of ℱ does not have the Baire property in X.},
author = {Mats Aigner, Vitalij A. Chatyrko, Venuste Nyagahakwa},
journal = {Colloquium Mathematicae},
keywords = {Vitali set; Baire property; admissible extension of a topology},
language = {eng},
number = {2},
pages = {179-187},
title = {On countable families of sets without the Baire property},
url = {http://eudml.org/doc/283890},
volume = {133},
year = {2013},
}

TY - JOUR
AU - Mats Aigner
AU - Vitalij A. Chatyrko
AU - Venuste Nyagahakwa
TI - On countable families of sets without the Baire property
JO - Colloquium Mathematicae
PY - 2013
VL - 133
IS - 2
SP - 179
EP - 187
AB - We suggest a method of constructing decompositions of a topological space X having an open subset homeomorphic to the space (ℝⁿ,τ), where n is an integer ≥ 1 and τ is any admissible extension of the Euclidean topology of ℝⁿ (in particular, X can be a finite-dimensional separable metrizable manifold), into a countable family ℱ of sets (dense in X and zero-dimensional in the case of manifolds) such that the union of each non-empty proper subfamily of ℱ does not have the Baire property in X.
LA - eng
KW - Vitali set; Baire property; admissible extension of a topology
UR - http://eudml.org/doc/283890
ER -