Theorems · Theorem · general topology
Filter.subseq_tendsto_of_neBot
∀ {α : Type u_1} {f : Filter α} [f.IsCountablyGenerated] {u : ℕ → α},
(f ⊓ Filter.map u Filter.atTop).NeBot → ∃ θ, StrictMono θ ∧ Filter.Tendsto (u ∘ θ) Filter.atTop f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Filter.IsCountablyGenerated
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- Filter.NeBotstatement and proof · cited by 853
- Filter.mapstatement and proof · cited by 819
- StrictMonostatement and proof · cited by 706
- Filter.Tendsto.compproof · cited by 560
- Filter.IsCountablyGeneratedstatement and proof · cited by 220
- StrictMono.tendsto_atTopproof · cited by 20
- Filter.strictMono_subseq_of_tendsto_atTopproof · cited by 2
- Filter.exists_seq_comp_tendstoproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- MapClusterPt.tendsto_subseqproof · cited by 1
- TopologicalSpace.FirstCountableTopology.tendsto_subseqproof · cited by 0