Profinite separation systems
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.
Cite
@article{arxiv.1804.01921,
title = {Profinite separation systems},
author = {Reinhard Diestel and Jay Lilian Kneip},
journal= {arXiv preprint arXiv:1804.01921},
year = {2025}
}
Comments
This is the extend version of this paper. The shorter journal version, v1 of this post, differs from this in that its main result, the compactness theorem for profinite separation systems, is more natural there and less technical. We need the stronger version proved here for applications in a future paper. The short version is due to appear in ORDER, 2019