Theorems · Theorem · general topology
Filter.tendsto_principal
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {l : Filter α} {s : Set β},
Filter.Tendsto f l (Filter.principal s) ↔ ∀ᶠ (a : α) in l, f a ∈ s- Defined in
- Mathlib.Order.Filter.Tendsto
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Set.ofPredproof · cited by 6,101
- Filter.Tendstostatement · cited by 3,814
- Filter.Eventuallystatement · cited by 3,134
- Filter.principalstatement · cited by 740
Cited by28
Results whose statement or proof uses this declaration.
- tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_withinproof · cited by 28
- ContinuousWithinAt.tendsto_nhdsWithinproof · cited by 16
- Filter.tendsto_atTop_atTop_of_monotoneproof · cited by 8
- Filter.tendsto_atBotproof · cited by 7
- IsCompact.isSeqCompactproof · cited by 6
- Filter.tendsto_iff_seq_tendstoproof · cited by 5
- TendstoLocallyUniformlyOn.smul₀_of_isBoundedUnderproof · cited by 4
- Bundle.Trivialization.tendsto_nhds_iffproof · cited by 3
- Filter.tendsto_atBot_atBot_of_monotoneproof · cited by 3
- IsExtrOn.hasLineDerivAt_eq_zeroproof · cited by 3
- TendstoLocallyUniformlyOn.inv₀_of_disjointproof · cited by 3
- isCountablyCompact_iff_seq_clusterPtproof · cited by 2