Theorems · Theorem · functional analysis
closure_subset_closedAbsConvexHull
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : SeminormedRing 𝕜] [inst_1 : SMul 𝕜 E] [inst_2 : AddCommMonoid E]
[inst_3 : PartialOrder 𝕜] [inst_4 : TopologicalSpace E] {s : Set E}, closure s ⊆ (closedAbsConvexHull 𝕜) s- Defined in
- Mathlib.Analysis.LocallyConvex.AbsConvex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- closurestatement · cited by 1,254
- SeminormedRingstatement and proof · cited by 446
- ClosureOperatorstatement · cited by 371
- closure_minimalproof · cited by 94
- closedAbsConvexHullstatement · cited by 10
- isClosed_closedAbsConvexHullproof · cited by 2
- subset_closedAbsConvexHullproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- closedAbsConvexHull_closure_eq_closedAbsConvexHullproof · cited by 0