Theorems · Definition · functional analysis

PointwiseConvergenceCLM.equivWeakDual

(𝕜 : Type u_3) →
  [inst : NormedField 𝕜] →
    (E : Type u_7) →
      [inst_1 : AddCommGroup E] →
        [inst_2 : TopologicalSpace E] → [inst_3 : Module 𝕜 E] → (E →Lₚₜ[𝕜] 𝕜) ≃L[𝕜] WeakDual 𝕜 E

The topology of pointwise convergence on E →Lₚₜ[𝕜] 𝕜 coincides with the weak-\* topology.

Defined in

Mathlib.Topology.Algebra.Module.Spaces.PointwiseConvergenceCLM

Cited by

2 results in Mathlib

Foundations

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

Assumes

NormedFieldAddCommGroupTopologicalSpaceModule