Duality and tangles of set separations

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.

Keywords

tangles, homology

2010 Mathematics Subject Classification

05C83

The full text of this article is unavailable through your IP address: 3.145.61.142

Received 20 September 2021

Accepted 7 July 2022

Published 7 November 2023