[[Projective space]]
# Dual projective space

The **dual projective space** $\op{\mathcal{S}}$ of an $n$-dimensional [[abstract projective space]] $\mathcal{S}$ has $(n-k-1)$-dimensional subspaces of $\mathcal{S}$ as its $k$-dimensional subspaces,
and the containment relation is reversed, #m/def/geo 
e.g. hyperplanes of $\mathcal{S}$ are the points of $\op{\mathcal{S}}$.
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 $\mathcal{S}$ also hold for its dual $\op{\mathcal{S}}$.[^2020]

[^2020]: 2020\. [[Sources/@kissFiniteGeometries2020|Finite geometries]], §4, p. 79


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