Theorems · Theorem · general topology
principal_nhdsKer_singleton
∀ {α : Type u_3} [inst : TopologicalSpace α] [AlexandrovDiscrete α] (a : α), Filter.principal (nhdsKer {a}) = nhds a- Defined in
- Mathlib.Topology.AlexandrovDiscrete
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 73 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 · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Filter.principalstatement · cited by 740
- nhdsKerstatement · cited by 53
- AlexandrovDiscretestatement and proof · cited by 45
- nhdsSet_singletonproof · cited by 19
- principal_nhdsKerproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Topology.IsUpperSet.nhds_eq_principal_Iciproof · cited by 1
- Topology.IsLowerSet.nhds_eq_principal_Iicproof · cited by 1
- nhds_basis_nhdsKer_singletonproof · cited by 0
- alexandrovDiscrete_iff_nhdsproof · cited by 0