Theorems · Definition · functional analysis

ContinuousLinearMap.toUniformConvergenceCLM

{𝕜₁ : Type u_1} →
  {𝕜₂ : Type u_2} →
    [inst : NormedField 𝕜₁] →
      [inst_1 : NormedField 𝕜₂] →
        (σ : 𝕜₁ →+* 𝕜₂) →
          {E : Type u_3} →
            (F : Type u_4) →
              [inst_2 : AddCommGroup E] →
                [inst_3 : Module 𝕜₁ E] →
                  [inst_4 : TopologicalSpace E] →
                    [inst_5 : AddCommGroup F] →
                      [inst_6 : Module 𝕜₂ F] →
                        [inst_7 : TopologicalSpace F] →
                          [inst_8 : IsTopologicalAddGroup F] →
                            [inst_9 : ContinuousConstSMul 𝕜₂ F] →
                              (𝔖 : Set (Set E)) → (E →SL[σ] F) ≃ₗ[𝕜₂] UniformConvergenceCLM σ F 𝔖

The linear equivalence that maps a continuous linear map to the type copy endowed with the uniform convergence topology.

Defined in

Mathlib.Topology.Algebra.Module.Spaces.UniformConvergenceCLM

Cited by

3 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousConstSMul