Theorems · Theorem · general topology
Filter.Tendsto.eventually_gt_atTop
∀ {α : Type u_3} {β : Type u_4} [inst : Preorder β] [NoTopOrder 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
- 11 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Quot.sound
- Assumes
- PreorderNoTopOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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_gt_atTopproof · cited by 90
- NoTopOrderstatement and proof · cited by 50
Cited by11
Results whose statement or proof uses this declaration.
- Polynomial.zero_lt_eval_of_roots_lt_of_leadingCoeff_nonnegproof · cited by 3
- Filter.tendsto_const_mul_pow_atTop_iffproof · cited by 2
- AkraBazziRecurrence.isBigO_apply_r_sub_bproof · cited by 2
- Monotone.isBoundedUnder_le_comp_iffproof · cited by 2
- AddCircle.ae_empty_or_univ_of_forall_vadd_ae_eq_selfproof · cited by 2
- AkraBazziRecurrence.eventually_r_posproof · cited by 2
- Filter.tendsto_const_mul_atTop_iff_posproof · cited by 2
- AkraBazziRecurrence.eventually_log_b_mul_posproof · cited by 1
- Complex.IsExpCmpFilter.isLittleO_log_norm_reproof · cited by 1
- Function.locallyFinsuppWithin.finite_support_of_logCounting_isBigO_logproof · cited by 1
- PositiveLinearMap.exists_norm_apply_leproof · cited by 0