Theorems · Theorem · general topology

Filter.Tendsto.asymptoticNhds_vadd_const

∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : Field k] [inst_1 : LinearOrder k] [inst_2 : AddCommGroup V]
  [inst_3 : Module k V] [inst_4 : AddTorsor V P] [inst_5 : TopologicalSpace V] {α : Type u_4} {l : Filter α} {f : α → V}
  {v : V} (p : P),
  Filter.Tendsto f l (AffineSpace.asymptoticNhds k V v) →
    Filter.Tendsto (fun x => f x +ᵥ p) l (AffineSpace.asymptoticNhds k P v)

Defined in

Mathlib.Topology.Algebra.AsymptoticCone

Cited by

1 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderAddCommGroupModuleAddTorsorTopologicalSpace