Theorems · Theorem · general topology

le_of_tendsto

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : Preorder α] [ClosedIicTopology α] {f : β → α}
  {a b : α} {x : Filter β} [hx : x.NeBot], Filter.Tendsto f x (nhds a) → (∀ᶠ (c : β) in x, f c ≤ b) → a ≤ b

Defined in

Mathlib.Topology.Order.OrderClosed

Cited by

32 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpacePreorderClosedIicTopologyFilter.NeBot