Theorems · Theorem · field theory

IsUltrametricDist.isNonarchimedean_invariantExtension

∀ (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],
  IsNonarchimedean ⇑(IsUltrametricDist.invariantExtension K L)

The algebra norm invariantExtension is nonarchimedean.

Defined in: Mathlib.Analysis.Normed.Unbundled.InvariantExtension
Cited by: 1 results in Mathlib
Foundations: Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedField Field Algebra FiniteDimensional IsUltrametricDist

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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
Fieldstatement and proof · cited by 7,404
FiniteDimensionalstatement and proof · cited by 1,854
AlgEquivproof · cited by 1,681
le_rflproof · cited by 1,558
NormedFieldstatement and proof · cited by 1,084
le_transproof · cited by 985
IsUltrametricDiststatement and proof · cited by 177
IsNonarchimedeanstatement · cited by 77
ciSup_leproof · cited by 56

Cited by1

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isNonarchimedean_spectralNorm_of_finiteDimensional_normalproof · cited by 1