Theorems · Theorem · functional analysis

LinearMap.isBigOTVS_rev_comp

∀ {α : Type u_1} {𝕜 : Type u_3} {E : Type u_4} {F : Type u_5} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : AddCommGroup E] [inst_2 : TopologicalSpace E] [inst_3 : Module 𝕜 E] [inst_4 : AddCommGroup F]
  [inst_5 : TopologicalSpace F] [inst_6 : Module 𝕜 F] {l : Filter α} {f : α → E} (g : E →ₗ[𝕜] F),
  Filter.comap (⇑g) (nhds 0) ≤ nhds 0 → f =O[𝕜; l] (⇑g ∘ f)

Defined in

Mathlib.Analysis.Asymptotics.TVS

Cited by

2 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupTopologicalSpaceModuleAddCommGroupTopologicalSpaceModule