Theorems · Theorem · convex and discrete geometry
closure_subset_closedConvexHull
∀ {𝕜 : Type u_2} {E : Type u_3} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommGroup E]
[inst_3 : Module 𝕜 E] [inst_4 : TopologicalSpace E] {s : Set E}, closure s ⊆ (closedConvexHull 𝕜) s- Defined in
- Mathlib.Analysis.Convex.Topology
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- closurestatement · cited by 1,254
- ClosureOperatorstatement · cited by 371
- closure_minimalproof · cited by 94
- closedConvexHullstatement · cited by 10
- subset_closedConvexHullproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- closedConvexHull_closure_eq_closedConvexHullproof · cited by 0