Theorems · Definition · number theory
NumberField.mixedEmbedding.mixedSpaceOfRealSpace
{K : Type u_1} → [inst : Field K] → NumberField.mixedEmbedding.realSpace K →L[ℝ] NumberField.mixedEmbedding.mixedSpace KThe continuous linear map from realSpace K to mixedSpace K which is the identity at real
places and the natural map ℝ → ℂ at complex places.
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- RingHom.idstatement · cited by 18,349
- Fieldstatement and proof · cited by 7,404
- Complexstatement · cited by 5,565
- ContinuousLinearMapstatement · cited by 5,352
- ContinuousLinearMap.compproof · cited by 709
- NumberField.InfinitePlacestatement and proof · cited by 604
- NumberField.InfinitePlace.IsRealstatement and proof · cited by 301
- NumberField.InfinitePlace.IsComplexstatement and proof · cited by 272
- NumberField.mixedEmbedding.mixedSpacestatement · cited by 239
- NumberField.mixedEmbedding.realSpacestatement · cited by 87
- ContinuousLinearMap.projproof · cited by 77
Cited by20
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpacestatement · cited by 6
- NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasisstatement · cited by 3
- NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlacesstatement · cited by 3
- NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlacesstatement · cited by 2
- NumberField.mixedEmbedding.mixedSpaceOfRealSpace_applystatement · cited by 2
- NumberField.mixedEmbedding.fundamentalCone.normLeOne_eq_preimage_imageproof · cited by 2
- NumberField.mixedEmbedding.normAtAllPlaces_image_preimage_of_nonnegproof · cited by 2
- NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpacestatement and proof · cited by 2
- NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symmstatement · cited by 1
- NumberField.mixedEmbedding.volume_eq_two_pi_pow_mul_integralproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.logMap_expMapstatement and proof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iffstatement and proof · cited by 1