Theorems · Theorem · functional analysis

ContinuousAlternatingMap.compContinuousLinearMapCLM_apply

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {ι : Type u_4} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E]
  [inst_2 : Module 𝕜 E] [inst_3 : TopologicalSpace E] [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F]
  [inst_6 : TopologicalSpace F] [inst_7 : IsTopologicalAddGroup F] [inst_8 : ContinuousConstSMul 𝕜 F] {E' : Type u_6}
  [inst_9 : AddCommGroup E'] [inst_10 : Module 𝕜 E'] [inst_11 : TopologicalSpace E'] (f : E →L[𝕜] E')
  (g : E' [⋀^ι]→L[𝕜] F), (ContinuousAlternatingMap.compContinuousLinearMapCLM f) g = g.compContinuousLinearMap f

Defined in

Mathlib.Topology.Algebra.Module.Alternating.Topology

Cited by

3 results in Mathlib

Foundations

Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousConstSMulAddCommGroupModuleTopologicalSpace