Theorems · Theorem · functional analysis

UniformConvergenceCLM.completeSpace

∀ {𝕜₁ : Type u_1} {𝕜₂ : Type u_2} [inst : NormedField 𝕜₁] [inst_1 : NormedField 𝕜₂] (σ : 𝕜₁ →+* 𝕜₂) {E : Type u_3}
  (F : Type u_4) [inst_2 : AddCommGroup E] [inst_3 : Module 𝕜₁ E] [inst_4 : TopologicalSpace E]
  [inst_5 : AddCommGroup F] [inst_6 : Module 𝕜₂ F] [inst_7 : UniformSpace F] [inst_8 : IsUniformAddGroup F]
  [ContinuousSMul 𝕜₂ F] [CompleteSpace F] {𝔖 : Set (Set E)},
  Topology.IsCoherentWith 𝔖 → ⋃₀ 𝔖 = Set.univ → CompleteSpace (UniformConvergenceCLM σ F 𝔖)

Defined in

Mathlib.Topology.Algebra.Module.Spaces.UniformConvergenceCLM

Cited by

1 results in Mathlib

Foundations

Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleUniformSpaceIsUniformAddGroupContinuousSMulCompleteSpace