Theorems · Theorem · general topology

le_of_tendsto_of_tendsto_of_frequently

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : Preorder α] [t : OrderClosedTopology α] {f g : β → α}
  {b : Filter β} {a₁ a₂ : α},
  Filter.Tendsto f b (nhds a₁) → Filter.Tendsto g b (nhds a₂) → (∃ᶠ (x : β) in b, f x ≤ g x) → a₁ ≤ a₂

Defined in

Mathlib.Topology.Order.OrderClosed

Cited by

2 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpacePreorderOrderClosedTopology