Theorems · Theorem · general topology

MapClusterPt.liminf

∀ {α : Type u_2} {β : Type u_3} [inst : ConditionallyCompleteLinearOrder α] [inst_1 : TopologicalSpace α]
  [OrderTopology α] {u : β → α} {f : Filter β} [f.NeBot],
  autoParam (Filter.IsCoboundedUnder (fun x1 x2 => x1 ≥ x2) f u) MapClusterPt.liminf._auto_1 →
    autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≥ x2) f u) MapClusterPt.liminf._auto_3 →
      MapClusterPt (Filter.liminf u f) f u

The liminf of a function u along a filter f is a cluster point of u along f.

Defined in

Mathlib.Topology.Order.LiminfLimsup

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLinearOrderTopologicalSpaceOrderTopologyFilter.NeBot