Theorems · Theorem · convex and discrete geometry
StrictConvex.convex
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : TopologicalSpace E]
[inst_3 : AddCommMonoid E] [inst_4 : Module 𝕜 E] {s : Set E}, StrictConvex 𝕜 s → Convex 𝕜 s- Defined in
- Mathlib.Analysis.Convex.Strict
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 62 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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- Convexstatement · cited by 551
- interior_subsetproof · cited by 171
- StrictConvexstatement and proof · cited by 71
- convex_iff_pairwise_posproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- StrictConvex.addproof · cited by 2
- StrictConvex.centerMass_mem_interiorproof · cited by 2
- StrictConvex.ae_eq_const_or_average_mem_interiorproof · cited by 1
- strictConvex_iff_convexproof · cited by 1
- IsOpen.strictConvex_iffproof · cited by 0