论文标题
唐 - 弯曲 - 弯曲的二分法二分法
A Cantor--Bendixson dichotomy of domatic partitions
论文作者
论文摘要
令$γ= \ prod_ {i \ in \ mathbb {n}}γ_i$成为非平凡有限组的无限产物，或者让$γ=（\ Mathbb {r}/\ mathbb {z}）^n $是有限的二含量。对于一个无限的无限套件$ s \subseteqγ$，$ \ aleph_0 $ - domation分区是$γ$上的部分$ \ aleph_0 $ -coloring，因此$ s $ s $ s-neighborhood $ s \ cdot x $ cdot x $ inγ$ inγ$ inγ$中至少包含每个颜色的γ$。我们证明存在一个开放的$ \ aleph_0 $ dostic分区，如果存在可衡量的$ \ aleph_0 $ - domation分区，则存在$ s $的拓扑关闭。我们还调查了一般描述性组合设置中的命令分区。
Let $Γ=\prod_{i\in\mathbb{N}}Γ_i$ be an infinite product of nontrivial finite groups, or let $Γ=(\mathbb{R}/\mathbb{Z})^n$ be a finite-dimensional torus. For a countably infinite set $S\subseteq Γ$, an $\aleph_0$-domatic partition is a partial $\aleph_0$-coloring on $Γ$ such that the $S$-neighborhood $S\cdot x$ of every vertex $x\in Γ$ contains at least one instance of each color. We show that an open $\aleph_0$-domatic partition exists, iff a Baire measurable $\aleph_0$-domatic partition exists, iff the topological closure of $S$ is uncountable. We also investigate domatic partitions in the general descriptive combinatorics setting.
