Point at infinity

[1] In the real case, a point at infinity completes a line into a topologically closed curve.

In the case of a hyperbolic space, each line has two distinct ideal points.

[2] As a projective space over a field is a smooth algebraic variety, the same is true for the set of points at infinity.

All points at infinity together form the Cayley absolute or boundary of a hyperbolic plane.

This axiomatic symmetry grew out of a study of graphical perspective where a parallel projection arises as a central projection where the center C is a point at infinity, or figurative point.