Theorems · Theorem · general topology
UniformSpace.ext_iff
∀ {α : Type ua} {u₁ u₂ : UniformSpace α}, u₁ = u₂ ↔ ∀ (s : Set (α × α)), s ∈ uniformity α ↔ s ∈ uniformity α- Defined in
- Mathlib.Topology.UniformSpace.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- uniformitystatement and proof · cited by 765
- Filter.extproof · cited by 60
- UniformSpace.extproof · cited by 34
Cited by2
Results whose statement or proof uses this declaration.
- isUniformInducing_iff_uniformSpaceproof · cited by 3
- discreteUniformity_iff_eq_principal_setRelIdproof · cited by 1