Theorems · Theorem · real analysis
rightLim_eq_of_eq_bot
∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : TopologicalSpace β] [inst_2 : TopologicalSpace α]
[OrderTopology α] (f : α → β) {a : α}, nhdsWithin a (Set.Ioi a) = ⊥ → Function.rightLim f a = f a- Defined in
- Mathlib.Topology.Order.LeftRightLim
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Filterstatement · cited by 8,121
- Bot.botstatement and proof · cited by 4,720
- nhdsWithinstatement and proof · cited by 1,912
- Set.Ioistatement and proof · cited by 1,463
- OrderTopologystatement and proof · cited by 1,355
- Function.rightLimstatement · cited by 52
- leftLim_eq_of_eq_botproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- leftLim_rightLimproof · cited by 2
- variationOnFromTo.rightLim_eqproof · cited by 0