Theorems · Theorem · convex and discrete geometry

Convex.closure_interior_eq_closure_of_nonempty_interior

∀ {𝕜 : Type u_2} {E : Type u_3} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜]
  [inst_3 : AddCommGroup E] [inst_4 : Module 𝕜 E] [inst_5 : TopologicalSpace E] [IsTopologicalAddGroup E]
  [inst_7 : TopologicalSpace 𝕜] [OrderTopology 𝕜] [ContinuousSMul 𝕜 E] {s : Set E},
  Convex 𝕜 s → (interior s).Nonempty → closure (interior s) = closure s

Defined in

Mathlib.Analysis.Convex.Topology

Cited by

3 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupTopologicalSpaceOrderTopologyContinuousSMul