Theorems · Theorem · functional analysis

ContinuousLinearMap.isInducing_postcomp

∀ {𝕜₁ : Type u_1} {𝕜₂ : Type u_2} {𝕜₃ : Type u_3} [inst : NormedField 𝕜₁] [inst_1 : NormedField 𝕜₂]
  [inst_2 : NormedField 𝕜₃] {σ : 𝕜₁ →+* 𝕜₂} {τ : 𝕜₂ →+* 𝕜₃} {ρ : 𝕜₁ →+* 𝕜₃} [inst_3 : RingHomCompTriple σ τ ρ]
  {E : Type u_4} {F : Type u_5} {G : Type u_6} [inst_4 : AddCommGroup E] [inst_5 : Module 𝕜₁ E]
  [inst_6 : AddCommGroup F] [inst_7 : Module 𝕜₂ F] [inst_8 : AddCommGroup G] [inst_9 : Module 𝕜₃ G]
  [inst_10 : TopologicalSpace E] [inst_11 : TopologicalSpace F] [inst_12 : TopologicalSpace G]
  [inst_13 : IsTopologicalAddGroup F] [inst_14 : IsTopologicalAddGroup G] (f : F →SL[τ] G),
  Topology.IsInducing ⇑f → Topology.IsInducing f.comp

Defined in

Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap

Cited by

1 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNormedFieldNormedFieldRingHomCompTripleAddCommGroupModuleAddCommGroupModuleAddCommGroupModuleTopologicalSpaceTopologicalSpaceTopologicalSpaceIsTopologicalAddGroupIsTopologicalAddGroup