The sPACE of equivalence classes of vectors under non-zero scalar multiplication. Elements are sets of the form kv: k != 0, k scalar, v != O, v a vector where 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)