Theorems · Theorem · general topology
Filter.HasBasis.inseparable_iff_uniformity
∀ {α : Type u} [inst : UniformSpace α] {ι : Sort u_1} {p : ι → Prop} {s : ι → Set (α × α)},
(uniformity α).HasBasis p s → ∀ {x y : α}, Inseparable x y ↔ ∀ (i : ι), p i → (x, y) ∈ s i- Defined in
- Mathlib.Topology.UniformSpace.Separation
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 83 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.
Cites7
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
- UniformSpacestatement and proof · cited by 2,040
- uniformitystatement and proof · cited by 765
- Filter.HasBasisstatement and proof · cited by 604
- Inseparablestatement · cited by 160
- specializes_iff_inseparableproof · cited by 5
- Filter.HasBasis.specializes_iff_uniformityproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- inseparable_iff_clusterPt_uniformityproof · cited by 2
- CauchyFilter.inseparable_iffproof · cited by 1
- inseparable_iff_ker_uniformityproof · cited by 1
- eq_of_uniformity_basisproof · cited by 1
- UniformSpace.metrizable_uniformityproof · cited by 0