Theorems · Theorem · general topology
UniformSpace.Completion.comap_coe_eq_uniformity
∀ (α : Type u_1) [inst : UniformSpace α], Filter.comap (fun p => (↑p.1, ↑p.2)) (uniformity (UniformSpace.Completion α)) = uniformity α
- Defined in
- Mathlib.Topology.UniformSpace.Completion
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 90 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement · cited by 8,121
- UniformSpacestatement and proof · cited by 2,040
- uniformitystatement · cited by 765
- Filter.comapstatement · cited by 546
- UniformSpace.Completionstatement · cited by 192
- UniformSpace.Completion.coe'statement · cited by 144
- IsUniformInducing.comap_uniformityproof · cited by 22
- UniformSpace.Completion.isUniformInducing_coeproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- UniformSpace.Completion.isUniformEmbedding_coeproof · cited by 3
- UniformSpace.Completion.continuous_hatInvproof · cited by 1