Theorems · Theorem · general topology
Filter.Tendsto.eventually_ge_atTop
∀ {α : Type u_3} {β : Type u_4} [inst : Preorder β] {f : α → β} {l : Filter α},
Filter.Tendsto f l Filter.atTop → ∀ (c : β), ∀ᶠ (x : α) in l, c ≤ f x- Defined in
- Mathlib.Order.Filter.AtTopBot.Tendsto
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 and proof · cited by 3,814
- Filter.Eventuallystatement · cited by 3,134
- Filter.atTopstatement and proof · cited by 2,405
- Filter.Tendsto.eventuallyproof · cited by 174
- Filter.eventually_ge_atTopproof · cited by 111
Cited by22
Results whose statement or proof uses this declaration.
- Filter.Tendsto.atTop_mul_posproof · cited by 7
- Filter.Tendsto.nsmul_atTopproof · cited by 4
- locallyFinite_Icc_of_tendstoproof · cited by 3
- Monotone.upperBounds_range_comp_tendsto_atTopproof · cited by 3
- Filter.HasAntitoneBasis.comp_monoproof · cited by 2
- eventually_cobounded_le_normproof · cited by 2
- Filter.tendsto_const_mul_atTop_iff_posproof · cited by 2
- ProperSpace.of_seq_closedBallproof · cited by 2
- AkraBazziRecurrence.one_mem_range_sumCoeffsExpproof · cited by 1
- Filter.Tendsto.atTop_mul_atTopproof · cited by 1
- Asymptotics.IsLittleO.of_tendsto_div_atTopproof · cited by 1
- Complex.IsExpCmpFilter.isLittleO_log_norm_reproof · cited by 1