Theorems · Theorem · general topology
KuratowskiEmbedding.embeddingOfSubset_isometry
∀ {α : Type u} [inst : MetricSpace α] (x : ℕ → α), DenseRange x → Isometry (KuratowskiEmbedding.embeddingOfSubset x)When the reference set is dense, the embedding map is an isometry on its image.
- Defined in
- Mathlib.Topology.MetricSpace.Kuratowski
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- ENNRealstatement · cited by 9,879
- Top.topstatement · cited by 9,680
- AddSubgroupstatement · cited by 3,232
- le_reflproof · cited by 2,061
- absproof · cited by 1,814
- MetricSpacestatement and proof · cited by 1,684
- Dist.distproof · cited by 1,539
- le_of_ltproof · cited by 1,175
- add_le_addproof · cited by 666
- le_imp_le_of_le_of_leproof · cited by 576
- LE.le.antisymmproof · cited by 507
Cited by1
Results whose statement or proof uses this declaration.
- KuratowskiEmbedding.exists_isometric_embeddingproof · cited by 2