Theorems · Theorem · functional analysis

UniformConvergenceCLM.isVonNBounded_image2_apply

∀ {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] {R : Type u_6} [inst_7 : SeminormedRing R]
  [inst_8 : TopologicalSpace F] [inst_9 : IsTopologicalAddGroup F] [inst_10 : DistribMulAction R F]
  [inst_11 : ContinuousConstSMul R F] [inst_12 : SMulCommClass 𝕜₂ R F] {𝔖 : Set (Set E)}
  {S : Set (UniformConvergenceCLM σ F 𝔖)},
  Bornology.IsVonNBounded R S → ∀ {s : Set E}, s ∈ 𝔖 → Bornology.IsVonNBounded R (Set.image2 (fun f x => f x) S s)

Defined in

Mathlib.Topology.Algebra.Module.Spaces.UniformConvergenceCLM

Cited by

2 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleSeminormedRingTopologicalSpaceIsTopologicalAddGroupDistribMulActionContinuousConstSMulSMulCommClass