On special partitions of metric spaces

Partitions of non-complete Baire metric spaces

We investigate the properties of ideals associated with Kuratowski partitions of non-complete Baire metric spaces. We show that such an ideal can be precipitous.

关于度量空间中 Kuratowski 划分的注记

A note on Kuratowski partitions in metric spaces

本文证明了当 $κ$ 为不大于 $2^{\aleph_0}$ 的最小实值可测基数时，必然存在基数至多 $2^κ$ 且容许 Kuratowski 划分的完备度量空间。

Ramsey partitions of metric spaces

We investigate the existence of metric spaces which, for any coloring with a fixed number of colors, contain monochromatic isomorphic copies of a fixed starting space K. In the main theorem we construct such a space of size \(2^{\aleph_0}\) for colorings with \(\aleph_0\) colors and any metric space \(K\) of size \(\aleph_0\). We also give a slightly weaker theorem for countable ultrametric \(K\) where, however, the resulting space has size~\(\aleph_1\).

度量格的模型理论：伪有限划分格

The model theory of metric lattices: pseudofinite partition lattices

在度量结构模型理论下研究一般度量格，发展划分格的伪有限极限理论，并与连续极限理论建立联系。

Partition dimension and strong metric dimension of chain cycle

Let $G$ be a connected graph with vertex set $V(G)$ and edge set $E(G)$. For an ordered $k$-partition $Π=\{Q_1,\ldots,Q_k\}$ of $V(G)$, the representation of a vertex $v \in V(G)$ with respect to $Π$ is the $k$-vectors $r(v|Π)=(d(v,Q_1),\ldots,d(v,Q_k))$, where $d(v,Q_i)$ is the distance between $v$ and $Q_i$. The partition $Π$ is a resolving partition if $r(u|Π)\neq r(v|Π)$, for each pair of distinct vertices $u,v \in V(G)$. The minimum $k$ for which there is a resolving $k$-partition of $V(G)$ is the partition dimension of $G$. A vertex $w\in V(G)$ strongly resolves two distinct vertices $u,…