Theorems · Theorem · geometry

Affine.Simplex.closedInterior_eq_interior_union

∀ {k : Type u_1} {V : Type u_2} {P : Type u_4} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] [inst_4 : LinearOrder k] [IsOrderedAddMonoid k] [ZeroLEOneClass k] {n : ℕ}
  [inst_7 : NeZero n] (s : Affine.Simplex k P n), s.closedInterior = s.interior ∪ ⋃ i, (s.faceOpposite i).closedInterior

The closed interior is the union of the open interior and the surface.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic

Cited by

1 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsorLinearOrderIsOrderedAddMonoidZeroLEOneClassNeZero