Theorems · Definition · general topology
Metric.PiNatEmbed.embed
{ι : Type u_2} → (X : Type u_3) → (Y : ι → Type u_4) → (f : (i : ι) → X → Y i) → Metric.PiNatEmbed X Y f → (i : ι) → Y iX equipped with the distance coming from ∀ i, Y i embeds in ∀ i, Y i.
- Defined in
- Mathlib.Topology.MetricSpace.PiNat
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Metric.PiNatEmbedstatement and proof · cited by 20
- Metric.PiNatEmbed.ofPiNatproof · cited by 11
Cited by6
Results whose statement or proof uses this declaration.
- Metric.PiNatEmbed.isUniformEmbedding_embedstatement · cited by 2
- Metric.PiNatEmbed.emetricSpaceproof · cited by 2
- Metric.PiNatEmbed.isometry_embedstatement and proof · cited by 1
- Metric.PiNatEmbed.continuous_distDenseSeq_invproof · cited by 1
- Metric.PiNatEmbed.exists_embedding_to_hilbert_cubeproof · cited by 1
- Metric.PiNatEmbed.embed_injectivestatement and proof · cited by 0