Theorems · Definition · general topology
Filter.Subsingleton
{α : Type u_1} → Filter α → PropWe say that a filter is a subsingleton if there exists a subsingleton set that belongs to the filter.
- Defined in
- Mathlib.Order.Filter.Subsingleton
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Set.Subsingletonproof · cited by 276
Cited by16
Results whose statement or proof uses this declaration.
- Filter.EventuallyConstproof · cited by 93
- Filter.Subsingleton.mapstatement and proof · cited by 3
- Filter.subsingleton_iff_exists_le_purestatement · cited by 2
- Filter.Subsingleton.antistatement and proof · cited by 2
- Filter.Subsingleton.of_subsingletonstatement · cited by 2
- Filter.subsingleton_botstatement · cited by 1
- Filter.subsingleton_iff_bot_or_purestatement and proof · cited by 1
- Filter.subsingleton_iff_exists_singleton_memstatement · cited by 1
- Filter.HasBasis.subsingleton_iffstatement · cited by 1
- Filter.EventuallyEq.eventuallyConst_iffproof · cited by 1
- Filter.Subsingleton.exists_eq_purestatement and proof · cited by 1
- Filter.Subsingleton.prodstatement and proof · cited by 1