Theorems · Theorem · global analysis

tangentConeAt.lim_zero

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NormedDivisionRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
  [inst_3 : TopologicalSpace E] [ContinuousSMul 𝕜 E] {α : Type u_3} (l : Filter α) {c : α → 𝕜} {d : α → E} {y : E},
  Filter.Tendsto (fun n => ‖c n‖) l Filter.atTop →
    Filter.Tendsto (fun n => c n • d n) l (nhds y) → Filter.Tendsto d l (nhds 0)

Auxiliary lemma ensuring that, under the assumptions from an old definition of the tangent cone, the sequence d tends to 0 at infinity.

Defined in

Mathlib.Analysis.Calculus.TangentCone.Seq

Cited by

1 results in Mathlib

Foundations

Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedDivisionRingAddCommGroupModuleTopologicalSpaceContinuousSMul