Theorems · Theorem · general topology

isLUB_of_tendsto_atBot

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : Preorder α] [OrderClosedTopology α]
  [inst_3 : Preorder β] [IsCodirectedOrder β] [Nonempty β] {f : β → α} {a : α},
  Antitone f → Filter.Tendsto f Filter.atBot (nhds a) → IsLUB (Set.range f) a

Defined in

Mathlib.Topology.Order.MonotoneConvergence

Cited by

0 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpacePreorderOrderClosedTopologyPreorderIsCodirectedOrderNonempty