 Complex projective space CP"n" is also a compactification of C"n"; the Alexandroff one-point compactification of the plane C is (homeomorphic to) the complex projective line CP1, which in turn can be identified with a sphere, the Riemann sphere.Passing to projective space is a common tool in algebraic geometry because the added points at infinity lead to simpler formulations of many theorems.For example, any two different lines in RP2 intersect in precisely one point, a statement that is not true in R2.