Theorems · Definition · geometry

Projectivization.IsCollinear

{K : Type u_1} →
  {V : Type u_2} →
    [inst : DivisionRing K] → [inst_1 : AddCommGroup V] → [inst_2 : Module K V] → Set (Projectivization K V) → Prop

If there exists a submodule of dimension at most 2 containing all points in S, then S is collinear. The finite-dimensionality is required so that this notion is meaningful even when V is infinite-dimensional.

Defined in

Mathlib.LinearAlgebra.Projectivization.Collinear

Cited by

8 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule