Theorems · Definition · functional analysis

ContinuousLinearMap.toPointwiseConvergenceCLM

{𝕜₁ : Type u_4} →
  (𝕜₂ : Type u_5) →
    [inst : NormedField 𝕜₁] →
      [inst_1 : NormedField 𝕜₂] →
        (σ : 𝕜₁ →+* 𝕜₂) →
          (E : Type u_7) →
            (F : Type u_8) →
              [inst_2 : AddCommGroup E] →
                [inst_3 : TopologicalSpace E] →
                  [inst_4 : AddCommGroup F] →
                    [inst_5 : TopologicalSpace F] →
                      [inst_6 : IsTopologicalAddGroup F] →
                        [inst_7 : Module 𝕜₁ E] →
                          [inst_8 : Module 𝕜₂ F] →
                            [ContinuousSMul 𝕜₁ E] →
                              [inst_10 : ContinuousConstSMul 𝕜₂ F] → (E →SL[σ] F) →L[𝕜₂] E →SLₚₜ[σ] F

The topology of bounded convergence is stronger than the topology of pointwise convergence.

Defined in

Mathlib.Topology.Algebra.Module.Spaces.PointwiseConvergenceCLM

Cited by

3 results in Mathlib

Foundations

Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNormedFieldAddCommGroupTopologicalSpaceAddCommGroupTopologicalSpaceIsTopologicalAddGroupModuleModuleContinuousSMulContinuousConstSMul