Theorems · Theorem · general topology
nhds_eq_uniformity_prod
∀ {α : Type ua} [inst : UniformSpace α] {a b : α},
nhds (a, b) = (uniformity α).lift' fun s => {y | (y, a) ∈ s} ×ˢ {y | (b, y) ∈ s}- Defined in
- Mathlib.Topology.UniformSpace.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 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 and proof · cited by 8,121
- Set.ofPredstatement and proof · cited by 6,101
- nhdsstatement · cited by 5,554
- UniformSpacestatement and proof · cited by 2,040
- SProd.sprodstatement and proof · cited by 1,750
- uniformitystatement and proof · cited by 765
- SetRelstatement and proof · cited by 581
- Filter.lift'statement and proof · cited by 99
- nhds_prod_eqproof · cited by 84
- monotone_constproof · cited by 17
- Monotone.set_prodproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- nhdset_of_mem_uniformityproof · cited by 1