nLab
bornological coarse space

Contents

Definition

A bornological coarse space is a set XX equipped with a bornology BB and a coarse structure CC that are compatible: controlled thickenings of bounded subsets are bounded.

Here a U-controlled thickening (UX×XU\subset X\times X) of a subset BB of XX is the projection of X×BUX\times B\cap U onto its first factor.

A morphism of bornological coarse spaces is a map ff of sets that is controlled (for every UCU\in C we have (f×f)(U)C(f\times f)(U)\in C') and proper (for every BBB'\in B' we have f 1(B)Bf^{-1}(B')\in B).

Bornological coarse spaces can be used as a site with an interval? to construct motivic coarse spaces.

References

Last revised on July 15, 2016 at 05:17:35. See the history of this page for a list of all contributions to it.