Theorems · Theorem · functional analysis
LinearIsometry.isometry
∀ {R : Type u_1} {R₂ : Type u_2} {E : Type u_5} {E₂ : Type u_6} [inst : Semiring R] [inst_1 : Semiring R₂]
{σ₁₂ : R →+* R₂} [inst_2 : SeminormedAddCommGroup E] [inst_3 : SeminormedAddCommGroup E₂] [inst_4 : Module R E]
[inst_5 : Module R₂ E₂] (f : E →ₛₗᵢ[σ₁₂] E₂), Isometry ⇑f- Cited by
- 24 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, 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
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Isometrystatement · cited by 230
- LinearIsometrystatement and proof · cited by 194
- LinearIsometry.toLinearMapproof · cited by 55
- AddMonoidHomClass.isometry_of_normproof · cited by 18
- LinearIsometry.norm_mapproof · cited by 12
Cited by24
Results whose statement or proof uses this declaration.
- LinearIsometry.injectiveproof · cited by 11
- LinearIsometryEquiv.isometryproof · cited by 8
- LinearIsometry.continuousproof · cited by 4
- Complex.isometry_ofRealproof · cited by 4
- LinearIsometry.adjoint_comp_selfproof · cited by 2
- LinearIsometry.dist_mapproof · cited by 2
- LinearIsometry.isEmbeddingproof · cited by 1
- LinearIsometry.lipschitzproof · cited by 1
- LinearIsometry.antilipschitzproof · cited by 1
- RCLike.isUniformEmbedding_ofRealproof · cited by 1
- LinearIsometry.edist_mapproof · cited by 1
- Complex.isUniformEmbedding_ofRealproof · cited by 1