On countable families of sets without the Baire property
Volume 133 / 2013
Colloquium Mathematicum 133 (2013), 179-187
MSC: Primary 03E20; Secondary 54A10.
DOI: 10.4064/cm133-2-4
Abstract
We suggest a method of constructing decompositions of a topological space $X$ having an open subset homeomorphic to the space ($\mathbb R^n, \tau )$, where $n$ is an integer $\geq 1$ and $\tau $ is any admissible extension of the Euclidean topology of $\mathbb R^n$ (in particular, $X$ can be a finite-dimensional separable metrizable manifold), into a countable family $\mathcal F$ of sets (dense in $X$ and zero-dimensional in the case of manifolds) such that the union of each non-empty proper subfamily of $\mathcal F$ does not have the Baire property in $X$.
