Theorems · Theorem · functional analysis
AbsConvex.sInter
∀ {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 (Set E)}, (∀ s ∈ S, AbsConvex 𝕜 s) → AbsConvex 𝕜 (⋂₀ S)- Defined in
- Mathlib.Analysis.LocallyConvex.AbsConvex
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- SeminormedRingstatement and proof · cited by 446
- Set.sInterstatement · cited by 225
- AbsConvexstatement and proof · cited by 31
- convex_sInterproof · cited by 2
- Balanced.sInterproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- absConvexHullproof · cited by 29
- AbsConvex.iInterproof · cited by 1
- absConvexHull_eq_iInterproof · cited by 1
- absConvex_closed_sInterproof · cited by 0