Theorems · Theorem · real analysis

continuousWithinAt_rightLim_Ici

∀ {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.Ioi a)) (nhds (Function.rightLim f a)) →
    ContinuousWithinAt (Function.rightLim f) (Set.Ici a) a

Defined in: Mathlib.Topology.Order.LeftRightLim
Cited by: 0 results in Mathlib
Foundations: Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder TopologicalSpace TopologicalSpace OrderTopology T3Space

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

TopologicalSpacestatement and proof · cited by 24,529
LinearOrderstatement and proof · cited by 8,572
nhdsstatement and proof · cited by 5,554
Filter.Tendstostatement and proof · cited by 3,814
nhdsWithinstatement and proof · cited by 1,912
Set.Ioistatement and proof · cited by 1,463
OrderTopologystatement and proof · cited by 1,355
Set.Icistatement · cited by 1,070
ContinuousWithinAtstatement · cited by 512
Function.rightLimstatement and proof · cited by 52
T3Spacestatement and proof · cited by 51
continuousWithinAt_leftLim_Iicproof · cited by 2

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