Theorems · Theorem · general topology
nhds_basis_clopen
∀ {X : Type u_1} [inst : TopologicalSpace X] [T2Space X] [CompactSpace X] [TotallyDisconnectedSpace X] (x : X),
(nhds x).HasBasis (fun s => x ∈ s ∧ IsClopen s) id- Defined in
- Mathlib.Topology.Separation.Profinite
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- TopologicalSpacestatement and proof · cited by 24,529
- nhdsstatement and proof · cited by 5,554
- Set.univproof · cited by 3,945
- IsOpenproof · cited by 2,400
- IsClosedproof · cited by 1,639
- T2Spacestatement and proof · cited by 1,351
- Set.iInterproof · cited by 1,084
- Filter.HasBasisstatement · cited by 604
- CompactSpacestatement and proof · cited by 593
- Set.mem_univproof · cited by 416
- Set.inter_subset_leftproof · cited by 360
Cited by3
Results whose statement or proof uses this declaration.
- isTopologicalBasis_isClopenproof · cited by 5
- ProfiniteGrp.exist_openNormalSubgroup_sub_open_nhds_of_oneproof · cited by 5
- ProfiniteGrp.exist_openNormalAddSubgroup_sub_open_nhds_of_zeroproof · cited by 2