nLab coarse structure



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

The elements of CC are called entourages or controlled subsets.

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