Theorems · Theorem · general topology

tendsto_atTop_of_antitone

∀ {ι : Type u_3} {α : Type u_4} [inst : Preorder ι] [inst_1 : TopologicalSpace α]
  [inst_2 : ConditionallyCompleteLinearOrder α] [OrderTopology α] {f : ι → α},
  Antitone f → Filter.Tendsto f Filter.atTop Filter.atBot ∨ ∃ l, Filter.Tendsto f Filter.atTop (nhds l)

Defined in

Mathlib.Topology.Order.MonotoneConvergence

Cited by

4 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderTopologicalSpaceConditionallyCompleteLinearOrderOrderTopology