Theorems · Theorem · general topology

Monotone.ge_of_tendsto

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : Preorder α] [OrderClosedTopology α]
  [inst_3 : Preorder β] [IsDirectedOrder β] {f : β → α} {a : α},
  Monotone f → Filter.Tendsto f Filter.atTop (nhds a) → ∀ (b : β), f b ≤ a

Defined in

Mathlib.Topology.Order.MonotoneConvergence

Cited by

8 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpacePreorderOrderClosedTopologyPreorderIsDirectedOrder