Theorems · Theorem · real analysis
leftLim_eq_of_isBot
∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : TopologicalSpace β] {f : α → β} {a : α},
IsBot a → Function.leftLim f a = f a- Defined in
- Mathlib.Topology.Order.LeftRightLim
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderTopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Bot.botproof · cited by 4,720
- nhdsWithinproof · cited by 1,912
- OrderTopologyproof · cited by 1,355
- Set.Iioproof · cited by 1,166
- IsBotstatement and proof · cited by 77
- Function.leftLimstatement · cited by 60
- Preorder.topologyproof · cited by 24
- nhdsWithin_emptyproof · cited by 16
- leftLim_eq_of_eq_botproof · cited by 11
Cited by5
Results whose statement or proof uses this declaration.
- StieltjesFunction.measure_Iicproof · cited by 8
- BoundedVariationOn.vectorMeasure_singletonproof · cited by 1
- BoundedVariationOn.eVariationOn_Iic_eq_Iio_add_edistproof · cited by 1
- rightLim_eq_of_isTopproof · cited by 1
- StieltjesFunction.measure_botSetproof · cited by 0