论文标题
末端空间和树分类
End spaces and tree-decompositions
论文作者
论文摘要
我们提出了一个系统的研究，以了解有限粘附的树木分解如何捕获图形及其末端形成的空间的拓扑特性。作为主要结果，我们表征了何时可以区分图的末端，并表征了哪些末端的子集可以通过有限粘附的树分解来显示。尤其是，我们表明，当$ g $的末端的子集$ψ$可以通过有限粘合的树的分解显示，并且仅当$ψ$是$g_δ$（$ | g | $）的$g_δ$（$g_δ$），这是图与末端形成的拓扑空间。由于图形的未损失末端很容易被认为是$g_δ$，因此这为Carmesin的结果提供了一个结构性解释，即始终显示一组未损失的末端。
We present a systematic investigation into how tree-decompositions of finite adhesion capture topological properties of the space formed by a graph together with its ends. As main results, we characterise when the ends of a graph can be distinguished, and characterise which subsets of ends can be displayed by a tree-decomposition of finite adhesion. In particular, we show that a subset $Ψ$ of the ends of a graph $G$ can be displayed by a tree-decomposition of finite adhesion if and only if $Ψ$ is $G_δ$ (a countable intersection of open sets) in $|G|$, the topological space formed by a graph together with its ends. Since the undominated ends of a graph are easily seen to be $G_δ$, this provides a structural explanation for Carmesin's result that the set of undominated ends can always be displayed.
