Theorems · Theorem · general topology
Isometry.isometryEquivOnRange_toEquiv
∀ {α : Type u} {β : Type v} [inst : EMetricSpace α] [inst_1 : PseudoEMetricSpace β] {f : α → β} (h : Isometry f),
h.isometryEquivOnRange.toEquiv = Equiv.ofInjective f ⋯- Defined in
- Mathlib.Topology.MetricSpace.Isometry
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Equivstatement · cited by 8,337
- Set.Elemstatement · cited by 7,166
- Set.rangestatement · cited by 4,705
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EMetricSpacestatement and proof · cited by 242
- Isometrystatement and proof · cited by 230
- Equiv.ofInjectivestatement · cited by 64
- IsometryEquiv.toEquivstatement and proof · cited by 33
- Isometry.injectivestatement · cited by 11
- Isometry.isometryEquivOnRangestatement and proof · cited by 4
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