Theorems · Definition · functional analysis

toWeakSpaceCLM

(𝕜 : Type u_2) →
  (E : Type u_4) →
    [inst : CommSemiring 𝕜] →
      [inst_1 : TopologicalSpace 𝕜] →
        [inst_2 : ContinuousAdd 𝕜] →
          [inst_3 : ContinuousConstSMul 𝕜 𝕜] →
            [inst_4 : AddCommMonoid E] → [inst_5 : Module 𝕜 E] → [inst_6 : TopologicalSpace E] → E →L[𝕜] WeakSpace 𝕜 E

For a topological vector space E, "identity mapping" E → WeakSpace 𝕜 E is continuous. This definition implements it as a continuous linear map.

Defined in

Mathlib.Topology.Algebra.Module.Spaces.WeakDual

Cited by

5 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringTopologicalSpaceContinuousAddContinuousConstSMulAddCommMonoidModuleTopologicalSpace