The space of equivalence classes of vectors under non-zero scalar multiplication.Elements are sets of the formkv: k != 0, k scalar, v != O, v a vectorwhere O is the origin.v is a representative member of this equivalence class.The projective plane of a vector space is the collection of its 1-dimensional subspaces.The properties of the vector space induce a topology and notions of smoothness on the projective plane.A projective plane is in no meaningful sense a plane and would therefore be (but isn' t) better described as a "projective space".(1996-09-28)