Theorems · Theorem · global analysis

HasFDerivAtFilter.isThetaTVS_sub

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
  [inst_3 : TopologicalSpace E] {F : Type u_3} [inst_4 : NormedAddCommGroup F] [inst_5 : NormedSpace 𝕜 F] {f : E → F}
  {f' : E →L[𝕜] F} {L : Filter (E × E)},
  HasFDerivAtFilter f f' L → Topology.IsInducing ⇑f' → (fun p => f p.1 - f p.2) =Θ[𝕜; L] fun p => p.1 - p.2

Defined in

Mathlib.Analysis.Calculus.FDeriv.Basic

Cited by

4 results in Mathlib

Foundations

Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceNormedAddCommGroupNormedSpace