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 f l Filter.atTop → Filter.Tendsto (fun x => r * f x) l Filter.atBot

If a function f tends to infinity along a filter, then f multiplied by a negative constant (on the left) tends to negative infinity.

Defined in

Mathlib.Order.Filter.AtTopBot.Field

Cited by

9 results in Mathlib

Foundations

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

Assumes

FieldLinearOrderIsStrictOrderedRing