projective plane [prǝ`jek·tiv `plān] MATHEMATICS 1. The topological space obtained from the two-dimensional sphere by identifying antipodal points; the space of all lines through the origin in euclidean space. 2. More generally, a plane (in the sense of projective geometry) such that (1) every two points lie on exactly one line, (2) every two lines pass through exactly one point, and (3) there exists a four-point. |