Theorems · Theorem · general topology

exists_seq_tendsto_liminf

∀ {α : Type u_2} {β : Type u_3} [inst : ConditionallyCompleteLinearOrder α] [inst_1 : TopologicalSpace α]
  [OrderTopology α] [FirstCountableTopology α] {f : Filter β} [f.NeBot] {u : β → α} [f.IsCountablyGenerated],
  autoParam (Filter.IsCoboundedUnder (fun x1 x2 => x1 ≥ x2) f u) exists_seq_tendsto_liminf._auto_1 →
    autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≥ x2) f u) exists_seq_tendsto_liminf._auto_3 →
      ∃ x, Filter.Tendsto (u ∘ x) Filter.atTop (nhds (Filter.liminf u f)) ∧ Filter.Tendsto x Filter.atTop f

Defined in

Mathlib.Topology.Order.LiminfLimsup

Cited by

1 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLinearOrderTopologicalSpaceOrderTopologyFirstCountableTopologyFilter.NeBotFilter.IsCountablyGenerated