Theorems · Theorem · general topology
Filter.tendsto_atTop
∀ {α : Type u_3} {β : Type u_4} [inst : Preorder β] {m : α → β} {f : Filter α},
Filter.Tendsto m f Filter.atTop ↔ ∀ (b : β), ∀ᶠ (a : α) in f, b ≤ m a- Defined in
- Mathlib.Order.Filter.AtTopBot.Tendsto
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
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.
- Filterstatement and proof · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Filter.Tendstostatement · cited by 3,814
- Filter.Eventuallystatement and proof · cited by 3,134
- Filter.atTopstatement · cited by 2,405
Cited by24
Results whose statement or proof uses this declaration.
- Filter.tendsto_atTop_mono'proof · cited by 17
- Filter.not_isBoundedUnder_of_tendsto_atTopproof · cited by 4
- AkraBazziRecurrence.tendsto_atTop_rproof · cited by 4
- Filter.Tendsto.atTop_mul_const'proof · cited by 3
- Filter.Tendsto.atTop_of_add_constproof · cited by 3
- Filter.Tendsto.atTop_zsmul_constproof · cited by 3
- LinearGrowth.tendsto_atTop_of_linearGrowthInf_natCast_posproof · cited by 3
- Filter.Tendsto.exists_within_forall_leproof · cited by 3
- IsPreconnected.intermediate_value_Iciproof · cited by 3
- Filter.Tendsto.const_mul_atTop'proof · cited by 2
- Filter.Tendsto.atTop_of_const_addproof · cited by 2
- Filter.Tendsto.atTop_of_const_mulproof · cited by 2