Theorems · Theorem · functional analysis

ContinuousLinearMap.toPointwiseConvergenceCLM_apply

∀ {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 : ContinuousSMul 𝕜₁ E] [inst_10 : ContinuousConstSMul 𝕜₂ F] (x : E →SL[σ] F),
  (ContinuousLinearMap.toPointwiseConvergenceCLM 𝕜₂ σ E F) x = x

Defined in

Mathlib.Topology.Algebra.Module.Spaces.PointwiseConvergenceCLM

Cited by

2 results in Mathlib

Foundations

Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNormedFieldAddCommGroupTopologicalSpaceAddCommGroupTopologicalSpaceIsTopologicalAddGroupModuleModuleContinuousSMulContinuousConstSMul