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Theorems · Theorem · functional analysis

LinearMap.polar_nonempty

∀ {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) (s : Set E),
  (B.polar s).Nonempty
Defined in
Mathlib.Analysis.LocallyConvex.Polar
Cited by
1 results in Mathlib
Foundations
Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedCommRingAddCommMonoidAddCommMonoidModuleModule
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

StrongDual.polar_nonempty · cited by 0StrongDual.polar_nonemptySet · cited by 53352SetModule · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idAddCommMonoid · cited by 12281AddCommMonoidLinearMap · cited by 10215LinearMapSet.Nonempty · cited by 2627Set.NonemptyNormedCommRing · cited by 218NormedCommRingLinearMap.polar · cited by 23LinearMap.polarLinearMap.zero_mem_polar · cited by 3LinearMap.zero_mem_polarLinearMap.polar_nonemptyCITED BYCITES

Cites9

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Cited by1

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