Theorems · Definition · convex and discrete geometry
closedConvexHull
(𝕜 : Type u_2) →
{E : Type u_3} →
[inst : Semiring 𝕜] →
[PartialOrder 𝕜] → [inst_2 : AddCommGroup E] → [Module 𝕜 E] → [TopologicalSpace E] → ClosureOperator (Set E)The convex closed hull of a set s is the minimal convex closed set that includes s.
- Defined in
- Mathlib.Analysis.Convex.Topology
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- IsClosedproof · cited by 1,639
- Convexproof · cited by 551
- ClosureOperatorstatement · cited by 371
- ClosureOperator.ofCompletePredproof · cited by 4
- convex_closed_sInterproof · cited by 0
Cited by10
Results whose statement or proof uses this declaration.
- isClosed_closedConvexHullstatement and proof · cited by 2
- subset_closedConvexHullstatement and proof · cited by 2
- convexHull_subset_closedConvexHullstatement · cited by 1
- convex_closedConvexHullstatement and proof · cited by 1
- closedConvexHull_eq_closure_convexHullstatement · cited by 1
- closedConvexHull_minstatement · cited by 1
- closure_subset_closedConvexHullstatement · cited by 1
- closedConvexHull_closure_eq_closedConvexHullstatement and proof · cited by 0
- closedConvexHull_isClosedstatement and proof · cited by 0
- toWeakSpace_closedConvexHull_eqstatement and proof · cited by 0