Theorems · Theorem · convex and discrete geometry

segment_subset_closure_openSegment

∀ {𝕜 : Type u_2} {E : Type u_3} [inst : Ring 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] [DenselyOrdered 𝕜]
  [inst_4 : TopologicalSpace 𝕜] [OrderTopology 𝕜] [inst_6 : AddCommGroup E] [inst_7 : TopologicalSpace E]
  [ContinuousAdd E] [inst_9 : Module 𝕜 E] [ContinuousSMul 𝕜 E] {x y : E}, segment 𝕜 x y ⊆ closure (openSegment 𝕜 x y)

Defined in

Mathlib.Analysis.Convex.Topology

Cited by

2 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingLinearOrderIsStrictOrderedRingDenselyOrderedTopologicalSpaceOrderTopologyAddCommGroupTopologicalSpaceContinuousAddModuleContinuousSMul