Theorems · Theorem · convex and discrete geometry
closedConvexHull_eq_closure_convexHull
∀ {𝕜 : Type u_2} {E : Type u_3} [inst : Field 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommGroup E]
[inst_3 : Module 𝕜 E] [inst_4 : TopologicalSpace E] [IsTopologicalAddGroup E] [ContinuousConstSMul 𝕜 E] {s : Set E},
(closedConvexHull 𝕜) s = closure ((convexHull 𝕜) s)- Defined in
- Mathlib.Analysis.Convex.Topology
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Fieldstatement and proof · cited by 7,404
- PartialOrderstatement and proof · cited by 6,410
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- closurestatement · cited by 1,254
- ContinuousConstSMulstatement and proof · cited by 832
- ClosureOperatorstatement · cited by 371
- subset_closureproof · cited by 309
Cited by1
Results whose statement or proof uses this declaration.
- toWeakSpace_closedConvexHull_eqproof · cited by 0