Theorems · Theorem · general topology

locallyFinite_Icc_of_tendsto

∀ {X : Type u_1} [inst : LinearOrder X] [inst_1 : TopologicalSpace X] [OrderTopology X] {α : Type u_2}
  [inst_3 : LinearOrder α] [LocallyFiniteOrder α] [NoMaxOrder X] [NoMinOrder X] {f g : α → X},
  Filter.Tendsto f Filter.atTop Filter.atTop →
    Filter.Tendsto g Filter.atBot Filter.atBot → LocallyFinite fun n => Set.Icc (f n) (g n)

A family of closed intervals bounded by diverging limits is locally finite.

Defined in

Mathlib.Topology.Order.AtTopBotIxx

Cited by

3 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderTopologicalSpaceOrderTopologyLinearOrderLocallyFiniteOrderNoMaxOrderNoMinOrder