Theorems · Theorem · general topology

MapClusterPt.liminf_le

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

Every cluster point x of a function u along a filter f is greater than or equal to liminf u f.

Defined in

Mathlib.Topology.Order.LiminfLimsup

Cited by

0 results in Mathlib

Foundations

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

Assumes

ConditionallyCompleteLinearOrderTopologicalSpaceOrderTopology