Theorems · Theorem · general topology

tendsto_atTop_isLUB

∀ {α : Type u_1} {ι : Type u_3} [inst : Preorder ι] [inst_1 : TopologicalSpace α] [inst_2 : Preorder α]
  [SupConvergenceClass α] {f : ι → α} {a : α},
  Monotone f → IsLUB (Set.range f) a → Filter.Tendsto f Filter.atTop (nhds a)

Defined in

Mathlib.Topology.Order.MonotoneConvergence

Cited by

7 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Quot.sound

Assumes

PreorderTopologicalSpacePreorderSupConvergenceClass