Theorems · Theorem · convex and discrete geometry

Affine.Simplex.convexHull_eq_closedInterior

∀ {𝕜 : Type u_1} {V : Type u_2} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsOrderedRing 𝕜] [inst_3 : AddCommGroup V]
  [inst_4 : Module 𝕜 V] {n : ℕ} (s : Affine.Simplex 𝕜 V n), (convexHull 𝕜) (Set.range s.points) = s.closedInterior

The closed interior of a simplex is the convex hull of all vertices.

Defined in

Mathlib.Analysis.Convex.Combination

Cited by

1 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsOrderedRingAddCommGroupModule