Theorems · Definition · convex and discrete geometry
Convex
(𝕜 : Type u_1) → {E : Type u_2} → [Semiring 𝕜] → [PartialOrder 𝕜] → [AddCommMonoid E] → [SMul 𝕜 E] → Set E → PropConvexity of sets.
- Defined in
- Mathlib.Analysis.Convex.Basic
- Cited by
- 551 results in Mathlib
- Foundations
- Depth 13 from the axioms, rests on 121 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- StarConvexproof · cited by 62
Cited by579
Results whose statement or proof uses this declaration.
- ConvexOnproof · cited by 232
- convexHullproof · cited by 163
- ConcaveOnproof · cited by 159
- StrictConcaveOnproof · cited by 85
- StrictConvexOnproof · cited by 84
- convex_univstatement · cited by 53
- AbsConvexproof · cited by 31
- convex_ballstatement and proof · cited by 30
- convex_Iccstatement · cited by 29
- convex_Icistatement · cited by 29
- convexHull_minstatement · cited by 28
- QuasiconcaveOnproof · cited by 26
Showing the 200 most cited of 579.