Theorems · Theorem · real analysis

tendsto_leftLim_of_tendsto

∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : TopologicalSpace β] [inst_2 : TopologicalSpace α]
  [h'α : OrderTopology α] {f : α → β} {a : α},
  (∃ y, Filter.Tendsto f (nhdsWithin a (Set.Iio a)) (nhds y)) →
    Filter.Tendsto f (nhdsWithin a (Set.Iio a)) (nhds (Function.leftLim f a))

Defined in

Mathlib.Topology.Order.LeftRightLim

Cited by

5 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderTopologicalSpaceTopologicalSpaceOrderTopology