Theorems · Theorem · functional analysis
LinearMap.polar_zero
∀ {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), B.polar {0} = Set.univ- Defined in
- Mathlib.Analysis.LocallyConvex.Polar
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 103 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.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- 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.ofPredproof · cited by 6,101
- Norm.normproof · cited by 5,413
- Set.univstatement and proof · cited by 3,945
- map_zeroproof · cited by 1,614
- norm_zeroproof · cited by 366
- NormedCommRingstatement and proof · cited by 218
Cited by1
Results whose statement or proof uses this declaration.
- StrongDual.polar_zeroproof · cited by 0