Projectivization

A projectivization is one way of creating a projective space. Let $𝑉$ be a vector space over $𝕂$ . The projectivization $P (𝑉)$ is the orbit space $𝑉 ∖ {0} / 𝕂 \times$ of scalar multiplication by $𝕂 \times$ . #m/def/geo The following notations are used

P (𝕂 𝑛 + 1) = P 𝑛 𝕂 = P G (𝑛, 𝕂)

Projective points are thus equivalence classes of nonzero vectors related by scaling, and may be denoted by Homogenous coördinates. If $𝑉$ is a topological vector space, then $P (𝑉)$ is itself a topological space. If $𝕂$ is a Galois field, the projective space has a Galois geometry.

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