Year: 2026
Type: preprint
Abstract: We generalise the $σ$-ideal $\mathcal E$ generated by the closed Lebesgue null subsets of the Cantor space ${}^ω2$ to the context of higher Cantor spaces ${}^κ2$ for an uncountable cardinal $κ$ satisfying $κ=κ^{<κ}$. We introduce candidates for a higher closed null ideal based on slaloms on partitions of $κ$ into sets of size ${<}κ$, and study their combinatorial properties. We also give some relations between the cardinal characteristics of the higher closed null ideals and other cardinal characteristics.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220666909