Theorems · Theorem · general topology
Pi.uniformSpace_eq
∀ {ι : Type u_1} (α : ι → Type u) [U : (i : ι) → UniformSpace (α i)],
Pi.uniformSpace α = ⨅ i, UniformSpace.comap (Function.eval i) (U i)- Defined in
- Mathlib.Topology.UniformSpace.Pi
- Cited by
- 5 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- UniformSpacestatement and proof · cited by 2,040
- iInfstatement · cited by 1,690
- uniformityproof · cited by 765
- Function.evalstatement · cited by 140
- UniformSpace.comapstatement · cited by 61
- UniformSpace.extproof · cited by 34
Cited by5
Results whose statement or proof uses this declaration.
- Pi.uniformSpace_comap_precomp'proof · cited by 2
- ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLMproof · cited by 0
- UniformOnFun.isUniformInducing_pi_restrictproof · cited by 0
- cauchy_pi_iffproof · cited by 0
- cauchy_pi_iff'proof · cited by 0