Theorems · Theorem · functional analysis
ContinuousLinearMap.IsInvertible.injective
∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : TopologicalSpace M] [inst_1 : TopologicalSpace M₂]
[inst_2 : Semiring R] [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : AddCommMonoid M₂]
[inst_6 : Module R M₂] {f : M →L[R] M₂}, f.IsInvertible → Function.Injective ⇑f- Defined in
- Mathlib.Topology.Algebra.Module.Equiv
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- ContinuousLinearMapstatement and proof · cited by 5,352
- Function.Bijective.injectiveproof · cited by 115
- ContinuousLinearMap.IsInvertiblestatement and proof · cited by 104
- ContinuousLinearMap.IsInvertible.bijectiveproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- mdifferentiableWithinAt_of_isInvertible_mfderivWithinproof · cited by 2
- mdifferentiableAt_of_isInvertible_mfderivproof · cited by 0
- differentiableWithinAt_of_isInvertible_fderivWithinproof · cited by 0
- differentiableAt_of_isInvertible_fderivproof · cited by 0