Theorems · Theorem · general topology
Filter.isCountablyGenerated_seq
∀ {α : Type u_1} {ι' : Sort u_5} [Countable ι'] (x : ι' → Set α), (⨅ i, Filter.principal (x i)).IsCountablyGenerated- Defined in
- Mathlib.Order.Filter.CountablyGenerated
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Countable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.rangeproof · cited by 4,705
- iInfstatement and proof · cited by 1,690
- Filter.principalstatement and proof · cited by 740
- Countablestatement and proof · cited by 633
- Filter.IsCountablyGeneratedstatement · cited by 220
- Set.countable_rangeproof · cited by 31
- iInf_rangeproof · cited by 27
- Filter.generate_eq_biInfproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Filter.isCountablyGenerated_of_seqproof · cited by 1
- Filter.isCountablyGenerated_iff_exists_antitone_basisproof · cited by 0