Theorems · Theorem · general topology
Set.MapsTo.tendsto
∀ {α : Type u_1} {β : Type u_2} {s : Set α} {t : Set β} {f : α → β},
Set.MapsTo f s t → Filter.Tendsto f (Filter.principal s) (Filter.principal t)- Defined in
- Mathlib.Order.Filter.Tendsto
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Filter.Tendstostatement · cited by 3,814
- Filter.principalstatement · cited by 740
- Set.MapsTostatement and proof · cited by 732
- Filter.tendsto_principal_principalproof · cited by 15
Cited by11
Results whose statement or proof uses this declaration.
- PhragmenLindelof.quadrant_Iproof · cited by 4
- PhragmenLindelof.quadrant_IVproof · cited by 2
- PhragmenLindelof.vertical_stripproof · cited by 2
- tangentConeAt_mono_nhdsproof · cited by 2
- PhragmenLindelof.quadrant_IIproof · cited by 2
- PhragmenLindelof.quadrant_IIIproof · cited by 1
- AbsolutelyContinuousOnInterval.dist_le_of_pairwiseDisjoint_hasSumproof · cited by 1
- Filter.Tendsto.arccos_nhdsGEproof · cited by 0
- Filter.Tendsto.arccos_nhdsLEproof · cited by 0
- Filter.Tendsto.arcsin_nhdsGEproof · cited by 0
- Filter.Tendsto.arcsin_nhdsLEproof · cited by 0