Theorems · Theorem · functional analysis
absConvexHull_eq_self
∀ {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 ↔ AbsConvex 𝕜 s- Defined in
- Mathlib.Analysis.LocallyConvex.AbsConvex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- SeminormedRingstatement and proof · cited by 446
- ClosureOperatorstatement · cited by 371
- AbsConvexstatement · cited by 31
- absConvexHullstatement and proof · cited by 29
- ClosureOperator.isClosed_iffproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- AbsConvex.absConvexHull_eqproof · cited by 1