Theorems · Theorem · general topology

Filter.Tendsto.isBoundedUnder_le

∀ {ι : Type u_1} {α : Type u_2} [inst : Preorder α] [inst_1 : TopologicalSpace α] [BoundedLENhdsClass α] {f : Filter ι}
  {u : ι → α} {a : α}, Filter.Tendsto u f (nhds a) → Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) f u

Defined in

Mathlib.Topology.Order.LiminfLimsup

Cited by

25 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Quot.sound

Assumes

PreorderTopologicalSpaceBoundedLENhdsClass