Theorems · Theorem · functional analysis

UniformConvergenceCLM.topologicalSpace_mono

∀ {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] {𝔖₁ 𝔖₂ : Set (Set E)} [inst_7 : TopologicalSpace F]
  [inst_8 : IsTopologicalAddGroup F],
  𝔖₂ ⊆ 𝔖₁ → UniformConvergenceCLM.instTopologicalSpace σ F 𝔖₁ ≤ UniformConvergenceCLM.instTopologicalSpace σ F 𝔖₂

Defined in

Mathlib.Topology.Algebra.Module.Spaces.UniformConvergenceCLM

Cited by

1 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroup