Theorems · Theorem · general topology
closure_eq_inter_uniformity
∀ {α : Type ua} [inst : UniformSpace α] {t : SetRel α α}, closure t = ⋂ d ∈ uniformity α, SetRel.comp d (t.comp d)- Defined in
- Mathlib.Topology.UniformSpace.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 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
- UniformSpacestatement and proof · cited by 2,040
- closurestatement · cited by 1,254
- Set.iInterstatement and proof · cited by 1,084
- uniformitystatement and proof · cited by 765
- SetRelstatement and proof · cited by 581
- Set.iInter_congr_Propproof · cited by 170
- SetRel.compstatement and proof · cited by 136
- SetRel.comp_subset_compproof · cited by 10
- UniformSpace.hasBasis_symmetricproof · cited by 5
- SetRel.comp_subset_comp_leftproof · cited by 3
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