nLab coarse structure

Definition

In coarse geometry, a coarse structure on a set $X$ is a subset $C\subset P(X\times X)$ (of the power set of the Cartesian product of $X$ with itself) that contains the diagonal of $X$ and is closed under finite unions, subsets, relational compositions, and relational inverses. (Here composition is given by the fiber product over $X$, whereas inverses are obtained by permuting the two factors of $X$.)

The elements of $C$ are called entourages or controlled subsets.

Related concepts

• bornological coarse space