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Theorems · Theorem · general topology

Filter.Tendsto.eventually_lt_atBot

∀ {α : Type u_3} {β : Type u_4} [inst : Preorder β] [NoBotOrder β] {f : α → β} {l : Filter α},
  Filter.Tendsto f l Filter.atBot → ∀ (c : β), ∀ᶠ (x : α) in l, f x < c
Defined in
Mathlib.Order.Filter.AtTopBot.Tendsto
Cited by
2 results in Mathlib
Foundations
Depth 55 from the axioms · uses propext, Quot.sound
Assumes
PreorderNoBotOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.aecover_Ioi · cited by 5MeasureTheory.aecover_IoiMonotone.isBoundedUnder_ge_comp_iff · cited by 1Monotone.isBoundedUnder_g…Filter · cited by 8121FilterPreorder · cited by 7952PreorderFilter.Tendsto · cited by 3814Filter.TendstoFilter.Eventually · cited by 3134Filter.EventuallyFilter.atBot · cited by 512Filter.atBotFilter.Tendsto.eventually · cited by 174Tendsto.eventuallyNoBotOrder · cited by 43NoBotOrderFilter.eventually_lt_atBot · cited by 8Filter.eventually_lt_atBotTendsto.eventually_lt_atBotCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.