Theorems · Theorem · functional analysis

ContinuousLinearEquiv.continuousAlternatingMapCongr_apply

∀ {𝕜 : Type u_1} {E : Type u_2} {E' : Type u_3} {F : Type u_4} {G : Type u_5} {ι : Type u_6} [inst : NormedField 𝕜]
  [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E] [inst_3 : TopologicalSpace E] [inst_4 : AddCommGroup E']
  [inst_5 : Module 𝕜 E'] [inst_6 : TopologicalSpace E'] [inst_7 : AddCommGroup F] [inst_8 : Module 𝕜 F]
  [inst_9 : TopologicalSpace F] [inst_10 : IsTopologicalAddGroup F] [inst_11 : ContinuousConstSMul 𝕜 F]
  [inst_12 : AddCommGroup G] [inst_13 : Module 𝕜 G] [inst_14 : TopologicalSpace G] [inst_15 : IsTopologicalAddGroup G]
  [inst_16 : ContinuousConstSMul 𝕜 G] (e : E ≃L[𝕜] E') (e' : F ≃L[𝕜] G) (x : E [⋀^ι]→L[𝕜] F),
  (e.continuousAlternatingMapCongr e') x = (↑e').compContinuousAlternatingMap (x.compContinuousLinearMap ↑e.symm)

Defined in

Mathlib.Topology.Algebra.Module.Alternating.Topology

Cited by

1 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousConstSMulAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousConstSMul