Theorems · Theorem · general topology

eventually_le_limsup

∀ {α : Type u_2} {β : Type u_3} [inst : ConditionallyCompleteLinearOrder α] [inst_1 : TopologicalSpace α]
  [OrderTopology α] [FirstCountableTopology α] {f : Filter β} [CountableInterFilter f] {u : β → α},
  autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) f u) eventually_le_limsup._auto_1 →
    ∀ᶠ (b : β) in f, u b ≤ Filter.limsup u f

Defined in

Mathlib.Topology.Order.LiminfLimsup

Cited by

4 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLinearOrderTopologicalSpaceOrderTopologyFirstCountableTopologyCountableInterFilter