Separation systems are posets with additional structure that form an abstract setting in which tangle-like clusters in graphs, matroids and other combinatorial structures can be expressed and studied. This paper offers some basic theory about infinite separation systems and how they relate to the finite separation systems they induce. They can be used to prove tangle-type duality theorems for infinite graphs and matroids, which will be done in future work that will build on this paper.

中文翻译：

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Profinite 分离系统

分离系统是具有附加结构的偏序集，形成一个抽象设置，其中可以表达和研究图、拟阵和其他组合结构中的缠结状簇。本文提供了一些关于无限分离系统的基本理论，以及它们与它们所诱导的有限分离系统的关系。它们可用于证明无限图和拟阵的缠结型对偶定理，这将在基于本文的未来工作中完成。