Theorems · Theorem · general topology
UniformSpace.nhds_basis_clopens
∀ {X : Type u_1} [inst : UniformSpace X] [IsUltraUniformity X] (x : X),
(nhds x).HasBasis (fun s => x ∈ s ∧ IsClopen s) id- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- nhdsstatement · cited by 5,554
- UniformSpacestatement and proof · cited by 2,040
- le_rflproof · cited by 1,558
- uniformityproof · cited by 765
- Filter.HasBasisstatement · cited by 604
- SetRelproof · cited by 581
- IsClopenstatement and proof · cited by 189
- UniformSpace.ballproof · cited by 113
- SetRel.IsSymmproof · cited by 93
- SetRel.IsTransproof · cited by 21
- Filter.HasBasis.to_hasBasis'proof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- TopologicalSpace.isTopologicalBasis_clopensproof · cited by 0