The property of perspectivity in geometric group theory.

The coarse structure of a set is a good way to abstract the notion of quasi-isometry of metric spaces. This structure, when related to a Hausdorff locally compact paracompact space X, gives rise to a family of well-behaved compactifications of X. Many geometric examples such as visual boundaries of CAT(0) spaces, hyperbolic boundaries of delta-hyperbolic spaces and spaces admitting convergence group actions appear as boundaries of such compactifications. These compactifications agree with the coarse structure in the sense that if we consider two coarse equivalent spaces X and X', then there exists a correspondence between the compactifications of X and the compactifications of X'.