Theorems · Theorem · general topology
Metric.Sigma.isometry_mk
∀ {ι : Type u_1} {E : ι → Type u_2} [inst : (i : ι) → MetricSpace (E i)] (i : ι), Isometry (Sigma.mk i)The injection of a space in a disjoint union is an isometry
- Defined in
- Mathlib.Topology.MetricSpace.Gluing
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 152 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MetricSpacestatement and proof · cited by 1,684
- Dist.distproof · cited by 1,539
- Isometrystatement · cited by 230
- Isometry.of_dist_eqproof · cited by 27
- Metric.Sigma.dist_sameproof · cited by 3
- Metric.Sigma.metricSpacestatement · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Metric.Sigma.completeSpaceproof · cited by 0