Theorems · Theorem · general topology
closure_eq_uniformity
∀ {α : Type ua} [inst : UniformSpace α] (s : Set (α × α)),
closure s = ⋂ V ∈ {V | V ∈ uniformity α ∧ SetRel.IsSymm V}, (SetRel.comp V s).comp V- Defined in
- Mathlib.Topology.UniformSpace.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.ofPredstatement · cited by 6,101
- Set.extproof · cited by 2,266
- UniformSpacestatement and proof · cited by 2,040
- SProd.sprodproof · cited by 1,750
- closurestatement · cited by 1,254
- Set.iInterstatement · cited by 1,084
- uniformitystatement and proof · cited by 765
- Set.inter_commproof · cited by 291
- SetRel.compstatement · cited by 136
- UniformSpace.ballproof · cited by 113
Cited by2
Results whose statement or proof uses this declaration.
- uniformity_hasBasis_closedproof · cited by 4
- closure_eq_inter_uniformityproof · cited by 0