Theorems · Theorem · functional analysis
RingHom.isometry
∀ {𝕜₁ : Type u_4} {𝕜₂ : Type u_5} [inst : SeminormedRing 𝕜₁] [inst_1 : SeminormedRing 𝕜₂] (σ : 𝕜₁ →+* 𝕜₂)
[RingHomIsometric σ], Isometry ⇑σ- Defined in
- Mathlib.Analysis.Normed.Ring.Lemmas
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 153 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.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement and proof · cited by 10,189
- SeminormedRingstatement and proof · cited by 446
- RingHomIsometricstatement and proof · cited by 282
- Isometrystatement · cited by 230
- AddMonoidHomClass.isometry_of_normproof · cited by 18
- RingHomIsometric.norm_mapproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- Bornology.IsVonNBounded.imageproof · cited by 5
- HasDerivAt.comp_semilinearproof · cited by 2
- HasDerivAt.comp_ringHomproof · cited by 1
- LinearMap.isInducing_of_restrict_nhds_zeroproof · cited by 1