Theorems · Theorem · general topology
Filter.HasCountableBasis.isCountablyGenerated
∀ {α : Type u_1} {ι : Type u_4} {f : Filter α} {p : ι → Prop} {s : ι → Set α},
f.HasCountableBasis p s → f.IsCountablyGenerated- Defined in
- Mathlib.Order.Filter.CountablyGenerated
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.IsCountablyGeneratedstatement · cited by 220
- Set.Countable.imageproof · cited by 47
- Filter.HasCountableBasisstatement and proof · cited by 9
- Filter.HasCountableBasis.toHasBasisproof · cited by 3
- Filter.HasCountableBasis.countableproof · cited by 2
- Filter.HasBasis.eq_generateproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Filter.HasBasis.isCountablyGeneratedproof · cited by 2