Theorems · Theorem · convex and discrete geometry
ProperCone.dual_dual_flip
∀ {E : Type u_1} {F : Type u_2} [inst : TopologicalSpace E] [inst_1 : AddCommGroup E] [IsTopologicalAddGroup E]
[inst_3 : TopologicalSpace F] [inst_4 : AddCommGroup F] [inst_5 : Module ℝ E] [ContinuousSMul ℝ E]
[LocallyConvexSpace ℝ E] [inst_8 : Module ℝ F] (p : F →ₗ[ℝ] E →ₗ[ℝ] ℝ) [inst_9 : p.IsContPerfPair]
(C : ProperCone ℝ E), ProperCone.dual p ↑(ProperCone.dual p.flip ↑C) = CThe double dual of a proper cone is itself.
- Defined in
- Mathlib.Analysis.Convex.Cone.Dual
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- SetLike.coestatement · cited by 8,199
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- ContinuousSMulstatement and proof · cited by 1,016
- LinearMap.flipstatement and proof · cited by 193
- LocallyConvexSpacestatement and proof · cited by 81
- ProperConestatement and proof · cited by 57
Cited by1
Results whose statement or proof uses this declaration.
- PointedCone.minTensorProduct_eq_max_of_simplicial_generating_leftproof · cited by 1