Theorems · Definition · general topology
Filter.ker
{α : Type u_1} → Filter α → Set αThe kernel of a filter is the intersection of all its sets.
- Defined in
- Mathlib.Order.Filter.Defs
- Cited by
- 40 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Set.sInterproof · cited by 225
- Filter.setsproof · cited by 56
Cited by43
Results whose statement or proof uses this declaration.
- nhdsKerproof · cited by 53
- Filter.giPrincipalKerstatement · cited by 8
- ker_nhdsstatement · cited by 4
- Filter.HasBasis.kerstatement · cited by 4
- nhdsKer_iUnionproof · cited by 3
- Filter.ker_comapstatement · cited by 3
- nhdsKer_singleton_eq_ker_nhdsstatement and proof · cited by 3
- ker_nhds_eq_specializesstatement · cited by 3
- Filter.ker_principalstatement · cited by 3
- le_cofinite_iff_kerstatement and proof · cited by 2
- R0Space.closure_singletonstatement · cited by 2
- Filter.Tendsto.countable_compl_preimage_kerstatement · cited by 2