Theorems · Theorem · functional analysis

LinearMap.polar_univ

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 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.SeparatingRight → B.polar Set.univ = {0}

Defined in: Mathlib.Analysis.LocallyConvex.Polar
Cited by: 1 results in Mathlib
Foundations: Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NontriviallyNormedField AddCommMonoid AddCommMonoid Module Module

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Cites27

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
Realproof · 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
NontriviallyNormedFieldstatement and proof · cited by 8,742
Norm.normproof · cited by 5,413
Set.univstatement and proof · cited by 3,945
mul_oneproof · cited by 3,885
LT.lt.ne'proof · cited by 1,417

Cited by1

Results whose statement or proof uses this declaration.

StrongDual.polar_univproof · cited by 0