projective plane definition mathematics
The space of equivalence classes
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".