Theorems · Theorem · number theory

NumberField.mixedEmbedding.polarSpaceCoord_target

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K],
  (NumberField.mixedEmbedding.polarSpaceCoord K).target =
    ⇑(NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace K).symm ⁻¹'
      Set.univ ×ˢ Set.univ.pi fun i => Complex.polarCoord.target

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord
Cited by: 3 results in Mathlib
Foundations: Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites24

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement · cited by 62,936
Setstatement · cited by 53,352
Realstatement · cited by 25,697
Fieldstatement and proof · cited by 7,404
Complexstatement · cited by 5,565
Set.preimagestatement · cited by 4,946
Set.univstatement · cited by 3,945
SProd.sprodstatement · cited by 1,750
PartialHomeomorph.toPartialEquivstatement and proof · cited by 917
OpenPartialHomeomorph.toPartialHomeomorphstatement and proof · cited by 851
Homeomorphstatement · cited by 725
NumberFieldstatement and proof · cited by 653

Cited by3

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.lintegral_comp_polarSpaceCoord_symmproof · cited by 1
NumberField.mixedEmbedding.polarSpaceCoord_target'proof · cited by 1
NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symmproof · cited by 0