Theorems · Theorem · functional analysis

ContinuousLinearMap.completeSpace

∀ {𝕜₁ : Type u_1} {𝕜₂ : Type u_2} [inst : NormedField 𝕜₁] [inst_1 : NormedField 𝕜₂] {σ : 𝕜₁ →+* 𝕜₂} {E : Type u_4}
  {F : Type u_5} [inst_2 : AddCommGroup E] [inst_3 : Module 𝕜₁ E] [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜₂ F]
  [inst_6 : TopologicalSpace E] [inst_7 : UniformSpace F] [inst_8 : IsUniformAddGroup F] [ContinuousSMul 𝕜₂ F]
  [CompleteSpace F] [ContinuousSMul 𝕜₁ E],
  Topology.IsCoherentWith {s | Bornology.IsVonNBounded 𝕜₁ s} → CompleteSpace (E →SL[σ] F)

Defined in

Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap

Cited by

0 results in Mathlib

Foundations

Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNormedFieldAddCommGroupModuleAddCommGroupModuleTopologicalSpaceUniformSpaceIsUniformAddGroupContinuousSMulCompleteSpaceContinuousSMul