Theorems · Theorem · real analysis
rightLim_leftLim
∀ {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)) →
∀ [h' : (nhdsWithin a (Set.Ioi a)).NeBot], Function.rightLim (Function.leftLim f) a = Function.rightLim f a- Defined in
- Mathlib.Topology.Order.LeftRightLim
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites12
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
- Filter.NeBotstatement and proof · cited by 853
- Function.leftLimstatement · cited by 60
- Function.rightLimstatement and proof · cited by 52
- T3Spacestatement and proof · cited by 51
- leftLim_rightLimproof · cited by 2
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