Theorems · Theorem · general topology
map_uniformity_set_coe
∀ {α : Type ua} {s : Set α} [inst : UniformSpace α],
Filter.map (Prod.map Subtype.val Subtype.val) (uniformity ↑s) = uniformity α ⊓ Filter.principal (s ×ˢ s)- Defined in
- Mathlib.Topology.UniformSpace.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 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.
Cites12
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.Elemstatement and proof · cited by 7,166
- UniformSpacestatement and proof · cited by 2,040
- SProd.sprodstatement and proof · cited by 1,750
- Filter.mapstatement and proof · cited by 819
- uniformitystatement and proof · cited by 765
- Filter.principalstatement and proof · cited by 740
- Subtype.range_valproof · cited by 41
- Set.range_prodMapproof · cited by 19
- Filter.map_comapproof · cited by 10
- uniformity_setCoeproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- uniformContinuousOn_iff_restrictproof · cited by 8