Theorems · Theorem · general topology
kuratowskiEmbedding.isometry
∀ (α : Type u) [inst : MetricSpace α] [inst_1 : TopologicalSpace.SeparableSpace α], Isometry (kuratowskiEmbedding α)
The Kuratowski embedding is an isometry. Theorem 2.1 of [Assaf Naor, Metric Embeddings and Lipschitz Extensions][Naor-2015].
- Defined in
- Mathlib.Topology.MetricSpace.Kuratowski
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 235 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Isometrystatement · cited by 230
- PreLpstatement · cited by 163
- lpstatement · cited by 157
- TopologicalSpace.SeparableSpacestatement and proof · cited by 109
- kuratowskiEmbeddingstatement · cited by 5
- KuratowskiEmbedding.exists_isometric_embeddingproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- GromovHausdorff.eq_toGHSpace_iffproof · cited by 3
- GromovHausdorff.ghDist_le_hausdorffDistproof · cited by 3
- GromovHausdorff.toGHSpace_eq_toGHSpace_iff_isometryEquivproof · cited by 0
- GromovHausdorff.ghDist_eq_hausdorffDistproof · cited by 0