Theorems · Theorem · field theory
IsUltrametricDist.invariantExtension_extends
∀ (K : Type u_1) [inst : NormedField K] (L : Type u_2) [inst_1 : Field L] [inst_2 : Algebra K L] [h_fin : FiniteDimensional K L] [hu : IsUltrametricDist K] (x : K), (IsUltrametricDist.invariantExtension K L) ((algebraMap K L) x) = ‖x‖
The algebra norm invariantExtension extends the norm on K.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Norm.normstatement and proof · cited by 5,413
- Algebra.algebraMapstatement · cited by 4,706
- iSupproof · cited by 2,415
- FiniteDimensionalstatement and proof · cited by 1,854
- AlgEquivproof · cited by 1,681
- NormedFieldstatement and proof · cited by 1,084
- IsUltrametricDiststatement and proof · cited by 177
Cited by1
Results whose statement or proof uses this declaration.
- spectralNorm_extends_of_finiteDimensionalproof · cited by 0