Theorems · Theorem · functional analysis
IsConformalMap.injective
∀ {R : Type u_1} {N : Type u_3} {M' : Type u_5} [inst : NormedField R] [inst_1 : SeminormedAddCommGroup N]
[inst_2 : NormedSpace R N] [inst_3 : NormedAddCommGroup M'] [inst_4 : NormedSpace R M'] {f : M' →L[R] N},
IsConformalMap f → Function.Injective ⇑f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- ContinuousLinearMapstatement and proof · cited by 5,352
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NormedFieldstatement and proof · cited by 1,084
- LinearIsometryproof · cited by 194
- LinearIsometry.toContinuousLinearMapproof · cited by 47
- smul_right_injectiveproof · cited by 24
- IsConformalMapstatement and proof · cited by 21
- LinearIsometry.injectiveproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- IsConformalMap.ne_zeroproof · cited by 2