Non-meager free sets and independent families
| Autor: | Dušan Repovš, Andrea Medini, Lyubomyr Zdomskyy |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
meager relation
General Mathematics Existential quantification Mathematics::General Topology 01 natural sciences Combinatorics independent family FOS: Mathematics udc:515.122:510.3 Countable set 0101 mathematics Invariant (mathematics) completely Baire Axiom free set Mathematics Mathematics - General Topology Applied Mathematics 010102 general mathematics General Topology (math.GN) Mathematics - Logic 010101 applied mathematics Mathematics::Logic 54E50 54E52 03E05 03E50 Polish space Logic (math.LO) hereditarily Baire Subspace topology |
| Zdroj: | Proceedings of the American Mathematical Society, vol. 145, no. 9, pp. 4061-4073, 2017. |
| ISSN: | 0002-9939 |
| DOI: | 10.48550/arxiv.1508.00124 |
| Popis: | Our main result is that, given a collection $\mathcal{R}$ of meager relations on a Polish space $X$ such that $|\mathcal{R}|\leq\omega$, 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 "$|\mathcal{R}|\leq\omega$" with "$|\mathcal{R} Comment: 13 pages |
| Databáze: | OpenAIRE |
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