Theorems · Definition · functional analysis

PointwiseConvergenceCLM.inducingFn

{𝕜₁ : Type u_3} →
  {𝕜₂ : Type u_4} →
    [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 : Module 𝕜₁ E] →
                    [inst_5 : NormedAddCommGroup F] → [inst_6 : NormedSpace 𝕜₂ F] → (E →SLₚₜ[σ] F) →ₗ[𝕜₂] E → F

The coercion E →SLₚₜ[σ] F to E → F as a linear map. The topology on E →SLₚₜ[σ] F is induced by this map.

Defined in: Mathlib.Analysis.LocallyConvex.PointwiseConvergence
Cited by: 1 results in Mathlib
Foundations: Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedField NormedField AddCommGroup TopologicalSpace Module NormedAddCommGroup NormedSpace

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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 · cited by 18,349
NormedAddCommGroupstatement and proof · cited by 15,752
AddCommGroupstatement and proof · cited by 12,871
NormedSpacestatement and proof · cited by 12,499
LinearMapstatement · cited by 10,215
RingHomstatement and proof · cited by 10,189
Set.Elemstatement · cited by 7,166
Set.ofPredstatement · cited by 6,101

Cited by1

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PointwiseConvergenceCLM.isInducing_inducingFnstatement · cited by 1