Theorems · Theorem · convex and discrete geometry

Affine.Simplex.isClosed_closedInterior

∀ {𝕜 : Type u_4} {V : Type u_5} {P : Type u_6} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜]
  [inst_3 : TopologicalSpace 𝕜] [OrderClosedTopology 𝕜] [CompactIccSpace 𝕜] [ContinuousAdd 𝕜] [inst_7 : AddCommGroup V]
  [inst_8 : TopologicalSpace V] [IsTopologicalAddGroup V] [inst_10 : Module 𝕜 V] [ContinuousSMul 𝕜 V]
  [inst_12 : AddTorsor V P] [inst_13 : TopologicalSpace P] [IsTopologicalAddTorsor P] [T2Space P] {n : ℕ}
  (s : Affine.Simplex 𝕜 P n), IsClosed s.closedInterior

The closed interior of a simplex is a closed set.

Defined in

Mathlib.Analysis.Convex.Topology

Cited by

0 results in Mathlib

Foundations

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

Assumes

FieldLinearOrderIsStrictOrderedRingTopologicalSpaceOrderClosedTopologyCompactIccSpaceContinuousAddAddCommGroupTopologicalSpaceIsTopologicalAddGroupModuleContinuousSMulAddTorsorTopologicalSpaceIsTopologicalAddTorsorT2Space