Non-meager free sets and independent families MEDINI, ANDREA; REPOVŠ, DUŠAN; ZDOMSKYY, LYUBOMYR
Proceedings of the American Mathematical Society,
09/2017, Volume:
145, Issue:
9
Journal Article
Peer reviewed
Open access
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''.
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