Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets. First we characterise those tree sets that can be represented by tree sets arising from infinite trees; these are precisely those tree sets without a chain of order type ω + 1. Then we introduce and study a topological generalisation of infinite trees which can have limit edges, and show that every infinite tree set can be represented by the tree set admitted by a suitable such tree-like space.

中文翻译：

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无限树集的表示

树集是抽象结构，可用于在组合学中对各种树形对象进行建模。有限树集可以用有限图论树来表示。我们将此表示理论扩展到无限树集。首先我们刻画那些可以用无限树产生的树集表示的树集；这些正是那些没有 ω + 1 型序链的树集。 然后我们介绍并研究了具有极限边的无限树的拓扑推广，并证明了每个无限树集都可以由一个被承认的树集表示适合这样的树状空间。