Theorems · Theorem · number theory

NumberField.InfinitePlace.Completion.surjective_extensionEmbedding_of_isComplex

∀ {K : Type u_1} [inst : Field K] {v : NumberField.InfinitePlace K},
  v.IsComplex → Function.Surjective ⇑(NumberField.InfinitePlace.Completion.extensionEmbedding v)

If v is a complex infinite place, then the embedding v.Completion →+* ℂ is surjective.

Defined in: Mathlib.NumberTheory.NumberField.Completion.InfinitePlace
Cited by: 1 results in Mathlib
Foundations: Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field

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Cites12

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 · cited by 10,189
Fieldstatement and proof · cited by 7,404
Complexstatement · cited by 5,565
NumberField.InfinitePlacestatement and proof · cited by 604
NumberField.InfinitePlace.IsComplexstatement and proof · cited by 272
NumberField.InfinitePlace.Completionstatement · cited by 69
NumberField.InfinitePlace.Completion.extensionEmbeddingstatement · cited by 15
Complex.subfield_eq_of_closedproof · cited by 2
RingHom.fieldRange_eq_top_iffproof · cited by 2
NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbeddingproof · cited by 1
NumberField.InfinitePlace.Completion.subfield_ne_real_of_isComplexproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

NumberField.InfinitePlace.Completion.bijective_extensionEmbedding_of_isComplexproof · cited by 0