Theorems · Theorem · general topology

tendsto_atBot_ciInf

∀ {α : Type u_1} {ι : Type u_3} [inst : Preorder ι] [inst_1 : TopologicalSpace α]
  [inst_2 : ConditionallyCompletePartialOrderInf α] [InfConvergenceClass α] {f : ι → α},
  Monotone f → BddBelow (Set.range f) → Filter.Tendsto f Filter.atBot (nhds (⨅ i, f i))

Defined in

Mathlib.Topology.Order.MonotoneConvergence

Cited by

1 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderTopologicalSpaceConditionallyCompletePartialOrderInfInfConvergenceClass