Theorems · Definition · functional analysis

PointwiseConvergenceCLM.seminormFamily

{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] → SeminormFamily 𝕜₂ (E →SLₚₜ[σ] F) E

The family of seminorms that induce the topology of pointwise convergence, namely ‖A x‖ for all x : E.

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

NormedFieldNormedFieldAddCommGroupTopologicalSpaceModuleNormedAddCommGroupNormedSpace