Theorems · Theorem · general topology

Filter.Tendsto.limsup_eq

∀ {α : Type u_2} {β : Type u_3} [inst : ConditionallyCompleteLinearOrder α] [inst_1 : TopologicalSpace α]
  [OrderTopology α] {f : Filter β} {u : β → α} {a : α} [f.NeBot], Filter.Tendsto u f (nhds a) → Filter.limsup u f = a

If a function has a limit, then its limsup coincides with its limit.

Defined in

Mathlib.Topology.Order.LiminfLimsup

Cited by

12 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLinearOrderTopologicalSpaceOrderTopologyFilter.NeBot