Theorems · Theorem · general topology
Isometry.norm_map_of_map_zero
∀ {E : Type u_2} {F : Type u_3} [inst : SeminormedAddGroup E] [inst_1 : SeminormedAddGroup F] {f : E → F},
Isometry f → f 0 = 0 → ∀ (x : E), ‖f x‖ = ‖x‖- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Norm.normstatement and proof · cited by 5,413
- Dist.distproof · cited by 1,539
- SeminormedAddGroupstatement and proof · cited by 331
- Isometrystatement and proof · cited by 230
- dist_zero_rightproof · cited by 172
- Isometry.dist_eqproof · cited by 21
Cited by13
Results whose statement or proof uses this declaration.
- norm_mapproof · cited by 20
- CommCStarAlgebra.norm_add_eq_maxproof · cited by 3
- norm_cfcHomproof · cited by 2
- Unitization.lipschitzWith_addEquivproof · cited by 2
- norm_cfcₙHomproof · cited by 2
- Polynomial.leadingCoeff_le_mapMahlerMeasureproof · cited by 1
- continuous_cfcHomSuperset_leftproof · cited by 1
- continuous_cfcₙHomSuperset_leftproof · cited by 1
- Isometry.nnnorm_map_of_map_zeroproof · cited by 1
- Polynomial.mapMahlerMeasure_constproof · cited by 0
- Polynomial.mapMahlerMeasure_le_sum_norm_coeffproof · cited by 0
- Polynomial.norm_coeff_le_choose_mul_mapMahlerMeasureproof · cited by 0