Theorems · Definition · general topology
kuratowskiEmbedding
(α : Type u) → [inst : MetricSpace α] → [TopologicalSpace.SeparableSpace α] → α → ↥(lp (fun x => ℝ) ⊤)
The Kuratowski embedding is an isometric embedding of a separable metric space in ℓ^∞(ℕ, ℝ).
- Defined in
- Mathlib.Topology.MetricSpace.Kuratowski
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 234 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- ENNRealstatement · cited by 9,879
- Top.topstatement · cited by 9,680
- AddSubgroupstatement · cited by 3,232
- MetricSpacestatement and proof · cited by 1,684
- PreLpstatement · cited by 163
- lpstatement · cited by 157
- TopologicalSpace.SeparableSpacestatement and proof · cited by 109
- KuratowskiEmbedding.exists_isometric_embeddingproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- NonemptyCompacts.kuratowskiEmbeddingproof · cited by 4
- kuratowskiEmbedding.isometrystatement · cited by 4
- GromovHausdorff.eq_toGHSpace_iffproof · cited by 3
- GromovHausdorff.ghDist_le_hausdorffDistproof · cited by 3
- GromovHausdorff.ghDist_eq_hausdorffDistproof · cited by 0
- GromovHausdorff.toGHSpace_eq_toGHSpace_iff_isometryEquivproof · cited by 0