Complex projective space
![The Riemann sphere, the one-dimensional complex projective space, i.e. the complex projective line.](/Images/godic/202501/05/Stereographic_projection_in_3D5121.png")
![Parallel lines in the plane intersect at the vanishing point in the line at infinity.](/Images/godic/202501/05/Railroad-Tracks-Perspective5121.jpg")
In mathematics, complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real projective space label the lines through the origin of a real Euclidean space, the points of a complex projective space label the complex lines through the origin of a complex Euclidean space (see below for an intuitive account). Formally, a complex projective space is the space of complex lines through the origin of an (n+1)-dimensional complex vector space. The space is denoted variously as P(C), Pn(C) or CP. When n = 1, the complex projective space CP is the Riemann sphere, and when n = 2, CP is the complex projective plane (see there for a more elementary discussion).