Theorems · Definition · geometry

Projectivization.equivSubmodule

(K : Type u_1) →
  (V : Type u_2) →
    [inst : DivisionRing K] →
      [inst_1 : AddCommGroup V] → [inst_2 : Module K V] → Projectivization K V ≃ { H // Module.finrank K ↥H = 1 }

The equivalence between the projectivization and the collection of subspaces of dimension 1.

Defined in

Mathlib.LinearAlgebra.Projectivization.Basic

Cited by

2 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule