20.500.12556/RUL-110517 Non-meager free sets and independent families 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". free set meager relation completely Baire hereditarily Baire independent family true false true Angleški jezik Ni določen Članek v reviji 2019-09-16 07:42:29 2019-09-16 07:42:30 2022-08-22 03:44:15 0000-00-00 00:00:00 2017 0 0 Str. 4061-4073 no. 9 Vol. 145 Sept. 2017 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.122:510.3 0002-9939 10.1090/proc/13513 18047577 2335236 RAZ_Medini_Andrea_i2017.pdf RAZ_Medini_Andrea_i2017.pdf 1 C8B2189D078CE3220F74094BFD804BCA 5b34c1930504a2c92610db46c3d9a657c383ea999b3db899bd4468c25ce0251d 23981b4c-a1b7-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=122185 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0