Theorems · Theorem · general topology
KuratowskiEmbedding.embeddingOfSubset_dist_le
∀ {α : Type u} [inst : MetricSpace α] (x : ℕ → α) (a b : α),
dist (KuratowskiEmbedding.embeddingOfSubset x a) (KuratowskiEmbedding.embeddingOfSubset x b) ≤ dist a bThe embedding map is always a semi-contraction.
- Defined in
- Mathlib.Topology.MetricSpace.Kuratowski
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 231 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.
Cites15
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
- Norm.normproof · cited by 5,413
- AddSubgroupstatement · cited by 3,232
- absproof · cited by 1,814
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement and proof · cited by 1,539
- dist_eq_normproof · cited by 182
- PreLpstatement · cited by 163
- lpstatement · cited by 157
- dist_nonnegproof · cited by 126
Cited by1
Results whose statement or proof uses this declaration.
- KuratowskiEmbedding.embeddingOfSubset_isometryproof · cited by 1