Theorems · Theorem · general topology
KuratowskiEmbedding.exists_isometric_embedding
∀ (α : Type u) [inst : MetricSpace α] [TopologicalSpace.SeparableSpace α], ∃ f, Isometry f
Every separable metric space embeds isometrically in ℓ^∞(ℕ).
- Defined in
- Mathlib.Topology.MetricSpace.Kuratowski
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 233 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement · cited by 25,697
- ENNRealstatement · cited by 9,879
- Top.topstatement · cited by 9,680
- Set.rangeproof · cited by 4,705
- Set.univproof · cited by 3,945
- AddSubgroupstatement · cited by 3,232
- Set.Nonemptyproof · cited by 2,627
- MetricSpacestatement and proof · cited by 1,684
- Set.Countableproof · cited by 545
- Set.mem_univproof · cited by 416
- Denseproof · cited by 359
Cited by3
Results whose statement or proof uses this declaration.
- kuratowskiEmbeddingproof · cited by 5
- kuratowskiEmbedding.isometryproof · cited by 4
- GromovHausdorff.ghDist_le_hausdorffDistproof · cited by 3