Theorems · Theorem · functional analysis
LinearMap.polar_singleton
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NormedCommRing 𝕜] [inst_1 : AddCommMonoid E]
[inst_2 : AddCommMonoid F] [inst_3 : Module 𝕜 E] [inst_4 : Module 𝕜 F] (B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜) {a : E},
B.polar {a} = {y | ‖(B a) y‖ ≤ 1}- Defined in
- Mathlib.Analysis.LocallyConvex.Polar
- Cited by
- 4 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- Set.ofPredstatement and proof · cited by 6,101
- Norm.normstatement and proof · cited by 5,413
- le_antisymmproof · cited by 2,068
- NormedCommRingstatement and proof · cited by 218
- Set.mem_singleton_iffproof · cited by 172
Cited by4
Results whose statement or proof uses this declaration.
- LinearMap.sInter_polar_finite_subset_eq_polarproof · cited by 1
- LinearMap.polar_zeroproof · cited by 1
- StrongDual.polar_singletonproof · cited by 1
- LinearMap.mem_polar_singletonproof · cited by 0