论文标题
路径空间I：Menger型结果
Path spaces I: A Menger-type result
论文作者
论文摘要
无限图是通过有限路径连接的，其点是有限的。那么，有限图的无限概括是什么样的？通常，借助拓扑来回答这个问题，例如如果是图形的空间。在这里，我们介绍了一个更具组合的答案，我们称之为路径空间，并证明了Menger定理的版本。由于有许多类似拓扑路径的物体会诱导路径空间，因此可以在各种设置中应用此结果。
Infinite graphs are finitary in the sense that their points are connected via finite paths. So what would an infinitary generalization of finite graphs look like? Usually this question is answered with the aid of topology, e.g. in the case of graph-like spaces. Here we introduce a more combinatorial answer, which we call path space, and prove a version of Menger's theorem for it. Since there are many topological path-like objects which induce path spaces, this result can be applied in a variety of settings.
