Abstract projective space

Projective correlation

A correlation of a projective space $S$ is a Collineätion $𝛼 : S \to S 𝐨 𝐩$ into the Dual projective space. #m/def/geo

Further terminology

A correlation which is an involution is a polarity.
The image of a point $𝑃$ under a polarity $𝛼$ is called the polar (hyperplane) $𝑃 𝛼$ , while the image of a hyperplane $H$ is called the pole (point) $H 𝛼$ .
If $𝑃 I 𝑄 𝛼$ then $𝑃$ and $𝑄$ are conjugate, if $𝑃 I 𝑃 𝛼$ it is self-conjugate.

Examples

Orthogonal complement polarity

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