projective plane
<mathematics> 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)