Theorems · Theorem · general topology

Filter.tendsto_const_mul_atTop_of_neg

∀ {α : Type u_1} {β : Type u_2} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] {l : Filter β}
  {f : β → α} {r : α}, r < 0 → (Filter.Tendsto (fun x => r * f x) l Filter.atTop ↔ Filter.Tendsto f l Filter.atBot)

If r is a negative constant, fun x ↦ r * f x tends to infinity along a filter l if and only if f tends to negative infinity along l.

Defined in

Mathlib.Order.Filter.AtTopBot.Field

Cited by

2 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRing