Theorems · Theorem · general topology

Filter.Tendsto.add_atBot

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : AddCommGroup α] [inst_2 : LinearOrder α]
  [IsOrderedAddMonoid α] [OrderTopology α] {l : Filter β} {f g : β → α} {C : α},
  Filter.Tendsto f l (nhds C) → Filter.Tendsto g l Filter.atBot → Filter.Tendsto (fun x => f x + g x) l Filter.atBot

In a linearly ordered additive commutative group with the order topology, if f tends to C and g tends to atBot then f + g tends to atBot.

Defined in

Mathlib.Topology.Order.LeftRightNhds

Cited by

1 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceAddCommGroupLinearOrderIsOrderedAddMonoidOrderTopology