论文标题
正常树近似无限图
Approximating infinite graphs by normal trees
论文作者
论文摘要
我们表明，每个连接的图形都可以通过普通树近似，最多可以在其末端附近的邻域来表达一些任意小的错误。这种近似正常树的存在具有组合性和拓扑性质的后果。 在组合侧，我们表明，一旦在两端的局部跨越树的正常树时，图就具有正常的生成树；也就是说，图形具有正常生成树的唯一障碍物是其邻居都没有正常的生成树的结尾。 在拓扑方面，我们证明了最终空间$ω（g）$以及空间$ | g | = g \cupΩ（g）$自然与图$ g $相关，总是是偏头。这为Diestel，Sprüssel和Polat提供了许多结果的统一证明，并回答了有关Polat的最终空间迁移率的开放问题。
We show that every connected graph can be approximated by a normal tree, up to some arbitrarily small error phrased in terms of neighbourhoods around its ends. The existence of such approximate normal trees has consequences of both combinatorial and topological nature. On the combinatorial side, we show that a graph has a normal spanning tree as soon as it has normal spanning trees locally at each end; i.e., the only obstruction for a graph to having a normal spanning tree is an end for which none of its neighbourhoods has a normal spanning tree. On the topological side, we show that the end space $Ω(G)$, as well as the spaces $|G| = G \cup Ω(G)$ naturally associated with a graph $G$, are always paracompact. This gives unified and short proofs for a number of results by Diestel, Sprüssel and Polat, and answers an open question about metrizability of end spaces by Polat.
