Theorems · Theorem · real analysis
mapClusterPt_leftLim
∀ {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), MapClusterPt (Function.leftLim f a) (nhdsWithin a (Set.Iic a)) f- Defined in
- Mathlib.Topology.Order.LeftRightLim
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- nhdsproof · cited by 5,554
- Bot.botproof · cited by 4,720
- Filter.Tendstoproof · cited by 3,814
- nhdsWithinstatement and proof · cited by 1,912
- OrderTopologystatement and proof · cited by 1,355
- Set.Iioproof · cited by 1,166
- Set.Iicstatement and proof · cited by 1,111
- Filter.NeBotproof · cited by 853
- Filter.mapproof · cited by 819
Cited by3
Results whose statement or proof uses this declaration.
- mapClusterPt_rightLimproof · cited by 2
- tendsto_leftLim_atTop_of_tendstoproof · cited by 2
- eVariationOn.eVariationOn_leftLim_leproof · cited by 1