Theorems · Theorem · functional analysis
absConvexHull_eq_empty
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : SeminormedRing 𝕜] [inst_1 : SMul 𝕜 E] [inst_2 : AddCommMonoid E]
[inst_3 : PartialOrder 𝕜] {s : Set E}, (absConvexHull 𝕜) s = ∅ ↔ s = ∅- Defined in
- Mathlib.Analysis.LocallyConvex.AbsConvex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- SeminormedRingstatement and proof · cited by 446
- ClosureOperatorstatement · cited by 371
- Set.subset_empty_iffproof · cited by 40
- absConvexHullstatement and proof · cited by 29
- subset_absConvexHullproof · cited by 7
- absConvexHull_emptyproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- absConvexHull_nonemptyproof · cited by 1