The ideal boundary of hyperbolic space, also called its boundary at infinity, is the set of equivalence classes of geodesic rays, where two rays belong to the same class when they remain a bounded distance apart. Its elements are ideal points.
The ideal boundary of 
is homeomorphic to the sphere 
. Adjoining it gives a compactification
of 
homeomorphic
to a closed ball of dimension 
. Every isometry
of 
extends to the ideal boundary.
