Theorems · Definition · general topology
Filter.principal
{α : Type u_1} → Set α → Filter αThe principal filter of s is the collection of all supersets of s.
- Defined in
- Mathlib.Order.Filter.Defs
- Cited by
- 740 results in Mathlib
- Foundations
- Depth 7 from the axioms, rests on 20 definitions · uses no axioms
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 · cited by 8,121
- Set.ofPredproof · cited by 6,101
- Set.subset_univproof · cited by 228
- Set.Subset.transproof · cited by 218
- Set.subset_interproof · cited by 74
Cited by790
Results whose statement or proof uses this declaration.
- Filter.atTopproof · cited by 2,405
- nhdsWithinproof · cited by 1,912
- IsCompactproof · cited by 1,282
- Filter.atBotproof · cited by 512
- Filter.cocompactproof · cited by 141
- IsMaxOnproof · cited by 114
- Filter.lift'proof · cited by 99
- IsMinOnproof · cited by 96
- Filter.le_principal_iffstatement and proof · cited by 87
- IsLindelofproof · cited by 85
- IsCompact.isClosedproof · cited by 77
- IsCompleteproof · cited by 68
Showing the 200 most cited of 790.