Theorems · Theorem · real analysis

leftLim_rightLim

∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : TopologicalSpace β] [inst_2 : TopologicalSpace α]
  [OrderTopology α] [T3Space β] {f : α → β} {a : α},
  Filter.Tendsto f (nhdsWithin a (Set.Iio a)) (nhds (Function.leftLim f a)) →
    ∀ [h' : (nhdsWithin a (Set.Iio a)).NeBot], Function.leftLim (Function.rightLim f) a = Function.leftLim f a

Defined in

Mathlib.Topology.Order.LeftRightLim

Cited by

2 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderTopologicalSpaceTopologicalSpaceOrderTopologyT3SpaceFilter.NeBot