Theorems · Inductive type · general topology
Metric.PiNatEmbed
{ι : Type u_2} → (X : Type u_5) → (Y : ι → Type u_6) → ((i : ι) → X → Y i) → Type u_5Given a type X and a sequence Y of metric spaces and a sequence f : : ∀ i, X → Y i of
separating functions, PiNatEmbed X Y f is a type synonym for X seen as a subset of ∀ i, Y i.
- Defined in
- Mathlib.Topology.MetricSpace.PiNat
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 0 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by32
Results whose statement or proof uses this declaration.
- Metric.PiNatEmbed.ofPiNatstatement and proof · cited by 11
- Metric.PiNatEmbed.embedstatement and proof · cited by 5
- Metric.PiNatEmbed.toPiNatEquivstatement · cited by 5
- Metric.PiNatEmbed.toPiNatHomeostatement · cited by 3
- Metric.PiNatEmbed.continuous_toPiNatstatement · cited by 2
- Metric.PiNatEmbed.emetricSpacestatement · cited by 2
- Metric.PiNatEmbed.isUniformEmbedding_embedstatement and proof · cited by 2
- Metric.PiNatEmbed.casesOnstatement and proof · cited by 1
- Metric.PiNatEmbed.continuous_distDenseSeq_invstatement and proof · cited by 1
- Metric.PiNatEmbed.exists_embedding_to_hilbert_cubeproof · cited by 1
- Metric.PiNatEmbed.extstatement and proof · cited by 1
- Metric.PiNatEmbed.isometry_embedstatement · cited by 1