Theorems · Definition · geometry

Projectivization.equivQuotientOrbitRel

(k : Type u_1) →
  (V : Type u_2) →
    [inst : DivisionRing k] →
      [inst_1 : AddCommGroup V] →
        [inst_2 : Module k V] → Projectivization k V ≃ Quotient (MulAction.orbitRel kˣ { v // v ≠ 0 })

ℙ k V is equivalent to the quotient of the non-zero elements of V by kˣ.

Defined in

Mathlib.LinearAlgebra.Projectivization.Cardinality

Cited by

0 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule