Theorems · Definition · convex and discrete geometry

Convex.toCone

Deprecated since 2026-03-30Mathlib marks this declaration as deprecated.

{𝕜 : Type u_1} →
  {M : Type u_4} →
    [inst : Field 𝕜] →
      [inst_1 : LinearOrder 𝕜] →
        [IsStrictOrderedRing 𝕜] →
          [inst_3 : AddCommGroup M] → [inst_4 : Module 𝕜 M] → (s : Set M) → Convex 𝕜 s → ConvexCone 𝕜 M

The set of vectors proportional to those in a convex set forms a convex cone.

Defined in

Mathlib.Geometry.Convex.Cone.Basic

Cited by

7 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingAddCommGroupModule