Theorems · Definition · functional analysis

PointwiseConvergenceCLM.evalCLM

{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] → [inst_9 : ContinuousConstSMul 𝕜₂ F] → E → (E →SLₚₜ[σ] F) →L[𝕜₂] F

The evaluation map (f : E →SLₚₜ[σ] F) ↦ f a for a : E as a continuous linear map.

Defined in: Mathlib.Topology.Algebra.Module.Spaces.PointwiseConvergenceCLM
Cited by: 1 results in Mathlib
Foundations: Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedField NormedField AddCommGroup TopologicalSpace AddCommGroup TopologicalSpace IsTopologicalAddGroup Module Module ContinuousConstSMul

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Setstatement · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
Modulestatement and proof · cited by 20,661
RingHom.idstatement and proof · cited by 18,349
AddCommGroupstatement and proof · cited by 12,871
LinearMapproof · cited by 10,215
RingHomstatement and proof · cited by 10,189
Set.Elemstatement · cited by 7,166
Set.ofPredstatement · cited by 6,101
ContinuousLinearMapstatement · cited by 5,352
Finitestatement · cited by 3,029

Cited by1

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PointwiseConvergenceCLM.evalCLM_applystatement and proof · cited by 0