Non-meager free sets and independent familiesMedini, Andrea (Avtor) Repovš, Dušan (Avtor) Zdomskyy, Lyubomyr (Avtor) free setmeager relationcompletely Bairehereditarily Baireindependent familyOur 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".20172019-09-16 07:42:29Članek v reviji110517sl