On countable families of sets without the Baire property
Colloquium Mathematicum, Tome 133 (2013) no. 2, pp. 179-187
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $X$.
Keywords:
suggest method constructing decompositions topological space having subset homeomorphic space mathbb tau where integer geq tau admissible extension euclidean topology mathbb particular finite dimensional separable metrizable manifold countable family mathcal sets dense zero dimensional manifolds union each non empty proper subfamily mathcal does have baire property
Affiliations des auteurs :
Mats Aigner 1 ; Vitalij A. Chatyrko 1 ; Venuste Nyagahakwa 2
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author = {Mats Aigner and Vitalij A. Chatyrko and Venuste Nyagahakwa},
title = {On countable families of sets without the {Baire} property},
journal = {Colloquium Mathematicum},
pages = {179--187},
publisher = {mathdoc},
volume = {133},
number = {2},
year = {2013},
doi = {10.4064/cm133-2-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm133-2-4/}
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Mats Aigner; Vitalij A. Chatyrko; Venuste Nyagahakwa. On countable families of sets without the Baire property. Colloquium Mathematicum, Tome 133 (2013) no. 2, pp. 179-187. doi: 10.4064/cm133-2-4
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