Theorems · Theorem · functional analysis

ContinuousLinearMap.precomp_apply

∀ {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 G] [inst_14 : ContinuousConstSMul 𝕜₃ G] [inst_15 : RingHomSurjective σ]
  [inst_16 : RingHomIsometric σ] (L : E →SL[σ] F) (f : F →SL[τ] G), (ContinuousLinearMap.precomp G L) f = f ∘SL L

Defined in

Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap

Cited by

0 results in Mathlib

Foundations

Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNormedFieldNormedFieldRingHomCompTripleAddCommGroupModuleAddCommGroupModuleAddCommGroupModuleTopologicalSpaceTopologicalSpaceTopologicalSpaceIsTopologicalAddGroupContinuousConstSMulRingHomSurjectiveRingHomIsometric