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  • Non-meager free sets and independent families
    Medini, Andrea ; Repovš, Dušan, 1954- ; Zdomskyy, Lyubomyr, 1983-
    Our main result is that, given a collection ▫$\mathcal{R}$▫ of meager relations on a Polish space ▫$X$▫ such that ▫$\vert\mathcal{R} \vert \leq \omega $▫, there exists a dense Baire subspace ▫$F$▫ of ... ▫$X$▫ (equivalently, a nowhere meager subset ▫$F$▫ of ▫$X$▫) such that ▫$F$▫ is ▫$R$▫-free for every ▫$R \in \mathcal{R}$▫. This generalizes a recent result of Banakh and Zdomskyy. As an application, we show that there exists a non-meager independent family on ▫$\omega$▫, and define the corresponding cardinal invariant. Furthermore, assuming Martin's Axiom for countable posets, our result can be strengthened by substituting "▫$\vert \mathcal{R} \vert \leq \omega$▫" with "▫$\vert \mathcal{R} \vert < \mathfrak{c}$▫" and "Baire" with "completely Baire".
    Source: Proceedings of the American Mathematical Society. - ISSN 0002-9939 (Vol. 145, no. 9, Sept. 2017, str. 4061-4073)
    Type of material - article, component part ; adult, serious
    Publish date - 2017
    Language - english
    COBISS.SI-ID - 18047577

    Link(s):

    http://doi.org/10.1090/proc/13513
    Repository of the University of Ljubljana – RUL
    DOI

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