Theorems · Theorem · general topology

ClusterPt.limsInf

∀ {α : Type u_2} [inst : ConditionallyCompleteLinearOrder α] [inst_1 : TopologicalSpace α] [OrderTopology α]
  {f : Filter α} [f.NeBot],
  autoParam (Filter.IsCobounded (fun x1 x2 => x1 ≥ x2) f) ClusterPt.limsInf._auto_1 →
    autoParam (Filter.IsBounded (fun x1 x2 => x1 ≥ x2) f) ClusterPt.limsInf._auto_3 → ClusterPt f.limsInf f

The limsInf of a filter f is a cluster point of f.

Defined in

Mathlib.Topology.Order.LiminfLimsup

Cited by

2 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLinearOrderTopologicalSpaceOrderTopologyFilter.NeBot