The dual projective space of an -dimensional abstract projective space has -dimensional subspaces of as its -dimensional subspaces,
and the containment relation is reversed, #m/def/geo
e.g. hyperplanes of are the points of .
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 also hold for its dual .1