Theorems · Theorem · general topology
Isometry.comp
∀ {α : Type u} {β : Type v} {γ : Type w} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β]
[inst_2 : PseudoEMetricSpace γ] {g : β → γ} {f : α → β}, Isometry g → Isometry f → Isometry (g ∘ f)The composition of isometries is an isometry.
- Defined in
- Mathlib.Topology.MetricSpace.Isometry
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Isometrystatement and proof · cited by 230
Cited by10
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingproof · cited by 4
- GromovHausdorff.eq_toGHSpace_iffproof · cited by 3
- GromovHausdorff.ghDist_le_hausdorffDistproof · cited by 3
- CommCStarAlgebra.norm_add_eq_maxproof · cited by 3
- NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingOfIsRealproof · cited by 2
- UniformFun.isometry_ofFun_continuousMapproof · cited by 1
- AffineIsometryEquiv.vadd_vsubproof · cited by 0
- GromovHausdorff.ghDist_eq_hausdorffDistproof · cited by 0
- NormedAddGroupHom.isometry_compproof · cited by 0
- Isometry.completion_mapproof · cited by 0