Projective space

Dual projective space

The dual projective space S𝐨𝐩 of an 𝑛-dimensional abstract projective space S has (𝑛 −𝑘 −1)-dimensional subspaces of S as its 𝑘-dimensional subspaces, and the containment relation is reversed, #m/def/geo e.g. hyperplanes of S are the points of S𝐨𝐩. By the principle of duality, any theorem stated in terms of incidence, subspaces, and containment which follows from the axioms of an abstract projective space S also hold for its dual S𝐨𝐩.¹

#state/develop | #lang/en | #SemBr