Theorems · Theorem · number theory

NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding

∀ {K : Type u_1} [inst : Field K] (v : NumberField.InfinitePlace K),
  IsClosed (Set.range ⇑(NumberField.InfinitePlace.Completion.extensionEmbedding v))

The embedding v.Completion →+* ℂ has closed image inside ℂ.

Defined in: Mathlib.NumberTheory.NumberField.Completion.InfinitePlace
Cited by: 1 results in Mathlib
Foundations: Depth 186 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
Set.rangestatement · cited by 4,705
IsClosedstatement · cited by 1,639
NumberField.InfinitePlacestatement and proof · cited by 604
NumberField.InfinitePlace.Completionstatement · cited by 69
Topology.IsClosedEmbedding.isClosed_rangeproof · cited by 41
Isometry.isClosedEmbeddingproof · cited by 15
NumberField.InfinitePlace.Completion.extensionEmbeddingstatement · cited by 15
NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingproof · cited by 4

Cited by1

Results whose statement or proof uses this declaration.

NumberField.InfinitePlace.Completion.surjective_extensionEmbedding_of_isComplexproof · cited by 1