Theorems · Theorem · general topology

tendsto_le_of_eventuallyLE

∀ {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} [hb : b.NeBot],
  Filter.Tendsto f b (nhds a₁) → Filter.Tendsto g b (nhds a₂) → f ≤ᶠ[b] g → a₁ ≤ a₂

Alias of le_of_tendsto_of_tendsto.

Defined in

Mathlib.Topology.Order.OrderClosed

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpacePreorderOrderClosedTopologyFilter.NeBot