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On countable families of sets without the Baire property

Tom 133 / 2013

Mats Aigner, Vitalij A. Chatyrko, Venuste Nyagahakwa Colloquium Mathematicum 133 (2013), 179-187 MSC: Primary 03E20; Secondary 54A10. DOI: 10.4064/cm133-2-4

Streszczenie

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 $X$.

Autorzy

  • Mats AignerDepartment of Mathematics
    Linköping University
    581 83 Linköping, Sweden
    e-mail
  • Vitalij A. ChatyrkoDepartment of Mathematics
    Linköping University
    581 83 Linköping, Sweden
    e-mail
  • Venuste NyagahakwaDepartment of Mathematics
    National University of Rwanda
    Butare, Rwanda
    e-mail

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