Profinite separation systems
Reinhard Diestel, Jay Lilian Kneip
TL;DR
This paper develops foundational theory for infinite separation systems, linking them to finite systems and setting the stage for future duality theorems in infinite graphs and matroids.
Contribution
It introduces basic theory for infinite separation systems and explores their relationship with finite systems, enabling future tangle-type duality results.
Findings
Establishes foundational properties of infinite separation systems
Links infinite systems to finite induced systems
Prepares groundwork for duality theorems in infinite structures
Abstract
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.
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