Theorems · Theorem · general topology
Filter.tendsto_atBot
∀ {α : Type u_3} {β : Type u_4} [inst : Preorder β] {m : α → β} {f : Filter α},
Filter.Tendsto m f Filter.atBot ↔ ∀ (b : β), ∀ᶠ (a : α) in f, m a ≤ b- Defined in
- Mathlib.Order.Filter.AtTopBot.Tendsto
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
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 · cited by 3,814
- Filter.Eventuallystatement and proof · cited by 3,134
- Filter.atBotstatement · cited by 512
- Set.mem_Iicproof · cited by 37
- Filter.tendsto_principalproof · cited by 28
- Filter.tendsto_iInfproof · cited by 13
Cited by7
Results whose statement or proof uses this declaration.
- IsPreconnected.intermediate_value_Iicproof · cited by 2
- Filter.tendsto_atBot_mono'proof · cited by 1
- StieltjesFunction.measure_Iic_of_tendsto_atBot_atBotproof · cited by 1
- Filter.not_isBoundedUnder_of_tendsto_atBotproof · cited by 0
- StieltjesFunction.isFiniteMeasure_of_forall_abs_leproof · cited by 0
- Filter.tendsto_sup_atBotproof · cited by 0
- Hyperreal.tendsto_atBot_iffproof · cited by 0