Theorems · Theorem · functional analysis

UniformConvergenceCLM.isUniformInducing_postcomp

∀ {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} {G : Type u_5} [inst_2 : AddCommGroup E] [inst_3 : Module 𝕜₁ E] [inst_4 : TopologicalSpace E]
  [inst_5 : AddCommGroup F] [inst_6 : Module 𝕜₂ F] [inst_7 : AddCommGroup G] [inst_8 : UniformSpace G]
  [inst_9 : IsUniformAddGroup G] {𝕜₃ : Type u_6} [inst_10 : NormedField 𝕜₃] [inst_11 : Module 𝕜₃ G] {τ : 𝕜₂ →+* 𝕜₃}
  {ρ : 𝕜₁ →+* 𝕜₃} [inst_12 : RingHomCompTriple σ τ ρ] [inst_13 : UniformSpace F] [inst_14 : IsUniformAddGroup F]
  (g : F →SL[τ] G), IsUniformInducing ⇑g → ∀ (𝔖 : Set (Set E)), IsUniformInducing g.comp

Defined in

Mathlib.Topology.Algebra.Module.Spaces.UniformConvergenceCLM

Cited by

4 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleAddCommGroupUniformSpaceIsUniformAddGroupNormedFieldModuleRingHomCompTripleUniformSpaceIsUniformAddGroup