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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-2-4,
author = {Mats Aigner and Vitalij A. Chatyrko and Venuste Nyagahakwa},
title = {On countable families of sets without the Baire property},
journal = {Colloquium Mathematicae},
volume = {131},
year = {2013},
pages = {179-187},
zbl = {1315.54026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-2-4}
}
Mats Aigner; Vitalij A. Chatyrko; Venuste Nyagahakwa. On countable families of sets without the Baire property. Colloquium Mathematicae, Tome 131 (2013) pp. 179-187. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-2-4/