An Ideal Zoo in the Baire Space
General Topology
2025-11-03 v1
Abstract
In this paper, we study the translations into the Baire space of several well-known -ideals and families originally defined on the Cantor space, using their combinatorial characterizations. These include the ideals of null sets, small sets, those generated by closed measure-zero sets, and the meager sets, leading to their "fake" analogues in the Baire space. We also parametrize families related to null sets by functions from . Several structural properties and relations between these families are investigated, including whether they form ideals, the existence of large chains and antichains, orthogonality, the -chain condition, and the determination of certain cardinal invariants.
Keywords
Cite
@article{arxiv.2510.27435,
title = {An Ideal Zoo in the Baire Space},
author = {Łukasz Mazurkiewicz and Marcin Michalski and Szymon Żeberski},
journal= {arXiv preprint arXiv:2510.27435},
year = {2025}
}