Theorems · Theorem · functional analysis

StrongDual.polarSubmodule_eq_setOfPred

∀ (𝕜 : Type u_4) [inst : NontriviallyNormedField 𝕜] {E : Type u_5} [inst_1 : AddCommMonoid E]
  [inst_2 : TopologicalSpace E] [inst_3 : Module 𝕜 E] {S : Type u_6} [inst_4 : SetLike S E]
  [inst_5 : SMulMemClass S 𝕜 E] (m : S), ↑(StrongDual.polarSubmodule 𝕜 m) = {y | ∀ x ∈ m, y x = 0}

Defined in

Mathlib.Analysis.LocallyConvex.Polar

Cited by

2 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommMonoidTopologicalSpaceModuleSetLikeSMulMemClass