Theorems · Theorem · general topology
Isometry.injective
∀ {α : Type u} {β : Type v} [inst : EMetricSpace α] [inst_1 : PseudoEMetricSpace β] {f : α → β},
Isometry f → Function.Injective fAn isometry from an emetric space is injective
- Defined in
- Mathlib.Topology.MetricSpace.Isometry
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- EMetricSpacestatement and proof · cited by 242
- Isometrystatement and proof · cited by 230
- Isometry.antilipschitzproof · cited by 14
- AntilipschitzWith.injectiveproof · cited by 8
Cited by12
Results whose statement or proof uses this declaration.
- AffineIsometry.injectiveproof · cited by 26
- LinearIsometry.injectiveproof · cited by 11
- Isometry.isometryEquivOnRangeproof · cited by 4
- Polynomial.leadingCoeff_le_mapMahlerMeasureproof · cited by 1
- gelfandTransform_bijectiveproof · cited by 1
- Isometry.isometryEquivOnRange_toEquivstatement · cited by 0
- Isometry.coveringNumber_imageproof · cited by 0
- Polynomial.norm_coeff_le_choose_mul_mapMahlerMeasureproof · cited by 0
- Unitization.splitMul_injectiveproof · cited by 0
- Polynomial.mapMahlerMeasure_le_sum_norm_coeffproof · cited by 0
- FormalMultilinearSeries.radius_compContinuousLinearMap_eqproof · cited by 0
- Polynomial.mapMahlerMeasure_pos_of_ne_zeroproof · cited by 0