Theorems · Theorem · functional analysis

ContinuousAlternatingMap.completeSpace

∀ {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 : UniformSpace F] [inst_7 : IsUniformAddGroup F] [ContinuousSMul 𝕜 E] [ContinuousConstSMul 𝕜 F]
  [CompleteSpace F], Topology.IsCoherentWith {s | Bornology.IsVonNBounded 𝕜 s} → CompleteSpace (E [⋀^ι]→L[𝕜] F)

Defined in

Mathlib.Topology.Algebra.Module.Alternating.Topology

Cited by

0 results in Mathlib

Foundations

Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleUniformSpaceIsUniformAddGroupContinuousSMulContinuousConstSMulCompleteSpace