Theorems · Theorem · convex and discrete geometry
IsOpen.strictConvex_iff
∀ {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}, IsOpen s → (StrictConvex 𝕜 s ↔ Convex 𝕜 s)- Defined in
- Mathlib.Analysis.Convex.Strict
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- IsOpenstatement and proof · cited by 2,400
- Convexstatement · cited by 551
- StrictConvexstatement · cited by 71
- StrictConvex.convexproof · cited by 5
- Convex.strictConvex_of_isOpenproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.