Theorems · Theorem · functional analysis

ContinuousLinearEquiv.arrowCongr_apply

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {G : Type u_4} {H : Type u_5} [inst : AddCommGroup E]
  [inst_1 : AddCommGroup F] [inst_2 : AddCommGroup G] [inst_3 : AddCommGroup H] [inst_4 : NormedField 𝕜]
  [inst_5 : Module 𝕜 E] [inst_6 : Module 𝕜 F] [inst_7 : Module 𝕜 G] [inst_8 : Module 𝕜 H] [inst_9 : TopologicalSpace E]
  [inst_10 : TopologicalSpace F] [inst_11 : TopologicalSpace G] [inst_12 : TopologicalSpace H]
  [inst_13 : IsTopologicalAddGroup G] [inst_14 : IsTopologicalAddGroup H] [inst_15 : ContinuousConstSMul 𝕜 G]
  [inst_16 : ContinuousConstSMul 𝕜 H] (e₁ : E ≃L[𝕜] F) (e₂ : H ≃L[𝕜] G) (f : E →L[𝕜] H) (x : F),
  ((e₁.arrowCongr e₂) f) x = e₂ (f (e₁.symm x))

Defined in

Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap

Cited by

0 results in Mathlib

Foundations

Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddCommGroupAddCommGroupAddCommGroupNormedFieldModuleModuleModuleModuleTopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceIsTopologicalAddGroupIsTopologicalAddGroupContinuousConstSMulContinuousConstSMul