Theorems · Theorem · real analysis

Monotone.tendsto_leftLim_within

∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : ConditionallyCompleteLinearOrder β]
  [inst_2 : TopologicalSpace β] [OrderTopology β] {f : α → β},
  Monotone f →
    ∀ [inst_4 : TopologicalSpace α] [OrderTopology α] (x : α),
      Filter.Tendsto f (nhdsWithin x (Set.Iio x)) (nhdsWithin (Function.leftLim f x) (Set.Iic (Function.leftLim f x)))

Defined in

Mathlib.Topology.Order.LeftRightLim

Cited by

2 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderConditionallyCompleteLinearOrderTopologicalSpaceOrderTopologyTopologicalSpaceOrderTopology