Theorems · Theorem · convex and discrete geometry

closure_openSegment

∀ {𝕜 : Type u_2} {E : Type u_3} [inst : Ring 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] [DenselyOrdered 𝕜]
  [inst_4 : PseudoMetricSpace 𝕜] [OrderTopology 𝕜] [ProperSpace 𝕜] [CompactIccSpace 𝕜] [inst_8 : AddCommGroup E]
  [inst_9 : TopologicalSpace E] [T2Space E] [ContinuousAdd E] [inst_12 : Module 𝕜 E] [ContinuousSMul 𝕜 E] (x y : E),
  closure (openSegment 𝕜 x y) = segment 𝕜 x y

Defined in

Mathlib.Analysis.Convex.Topology

Cited by

0 results in Mathlib

Foundations

Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingLinearOrderIsStrictOrderedRingDenselyOrderedPseudoMetricSpaceOrderTopologyProperSpaceCompactIccSpaceAddCommGroupTopologicalSpaceT2SpaceContinuousAddModuleContinuousSMul