Theorems · Theorem · general topology

ClusterPt.limsInf_le

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

Every cluster point x of a filter f is greater than or equal to f.limsInf.

Defined in

Mathlib.Topology.Order.LiminfLimsup

Cited by

1 results in Mathlib

Foundations

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

Assumes

ConditionallyCompleteLinearOrderTopologicalSpaceOrderTopology