# Duality and tangles of set separations

Reinhard Diestel, Christian Elbracht, Joshua Erde, Maximilian Teegen

Research output: Working paper

## Abstract

Applications of tangles of connectivity systems suggest a duality between these, in which for two sets $X$ and $Y\!$ the elements $x$ of $X$ map to subsets $Y_x$ of $Y\!$, and the elements $y$ of $Y\!$ map to subsets $X_y$ of $X$, so that $x\in X_y$ if and only if $y\in Y_x$ for all $x\in X$ and $y\in Y\!$. We explore this duality, and relate the tangles arising from the dual systems to each other.
Original language English 43 Published - 17 Sep 2021

## Keywords

• Tangles
• Seperation Systems
• Clustering

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