A canonical tree-of-tangles theorem for structurally submodular separation systems
Christian Elbracht, Jay Lilian Kneip
TL;DR
This paper proves that any structurally submodular separation system can be represented by a canonical tree set that effectively distinguishes its tangles, advancing the understanding of their structural properties.
Contribution
It introduces a canonical tree set construction for structurally submodular separation systems that uniquely distinguishes tangles, providing a new theoretical framework.
Findings
Existence of a canonical tree set for such systems
The tree set uniquely distinguishes tangles
Advances the structural theory of separation systems
Abstract
We show that every structurally submodular separation system admits a canonical tree set which distinguishes its tangles.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · Advanced Algebra and Logic