Cs> 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)
