Theorems · Theorem · convex and discrete geometry

Convex.Ioo_subset_of_mem_closure

∀ {𝕜 : Type u_4} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] [inst_3 : TopologicalSpace 𝕜]
  [OrderTopology 𝕜] {s : Set 𝕜}, Convex 𝕜 s → ∀ {a b : 𝕜}, a ∈ closure s → b ∈ closure s → Set.Ioo a b ⊆ s

Defined in

Mathlib.Analysis.Convex.Topology

Cited by

3 results in Mathlib

Foundations

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

Assumes

FieldLinearOrderIsStrictOrderedRingTopologicalSpaceOrderTopology