Mathlib Map

Theorems · Definition · number theory

NumberField.mixedEmbedding.fundamentalCone.expMap

{K : Type u_1} →
  [inst : Field K] →
    [NumberField K] →
      OpenPartialHomeomorph (NumberField.mixedEmbedding.realSpace K) (NumberField.mixedEmbedding.realSpace K)

The map from realSpace K → realSpace K whose components is given by expMap_single. It is, in some respect, a right inverse of logMap, see logMap_expMap.

Defined in
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne
Cited by
23 results in Mathlib
Foundations
Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldNumberField
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

NumberField.mixedEmbedding.fundamentalCone.expMapBasis · cited by 30fundamentalCone.expMapBas…NumberField.mixedEmbedding.fundamentalCone.expMapBasis_pos · cited by 7fundamentalCone.expMapBas…NumberField.mixedEmbedding.fundamentalCone.completeFamily · cited by 5fundamentalCone.completeF…NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne · cited by 3fundamentalCone.completeB…NumberField.mixedEmbedding.fundamentalCone.expMap_source · cited by 3fundamentalCone.expMap_so…NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply · cited by 2fundamentalCone.sum_expMa…NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply' · cited by 2fundamentalCone.expMapBas…NumberField.mixedEmbedding.fundamentalCone.injective_expMap · cited by 1fundamentalCone.injective…NumberField.mixedEmbedding.fundamentalCone.sum_eq_zero_of_mem_span_completeFamily · cited by 1fundamentalCone.sum_eq_ze…NumberField.mixedEmbedding.fundamentalCone.continuous_expMap · cited by 1fundamentalCone.continuou…NumberField.mixedEmbedding.fundamentalCone.logMap_expMap · cited by 1fundamentalCone.logMap_ex…NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply · cited by 1fundamentalCone.expMapBas…NumberField.mixedEmbedding.fundamentalCone.expMapBasis_source · cited by 1fundamentalCone.expMapBas…NumberField.mixedEmbedding.fundamentalCone.expMap_add · cited by 1fundamentalCone.expMap_addNumberField.mixedEmbedding.fundamentalCone.expMap_apply · cited by 1fundamentalCone.expMap_ap…Real · cited by 25697RealField · cited by 7404FieldOpenPartialHomeomorph · cited by 664OpenPartialHomeomorphNumberField · cited by 653NumberFieldNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceNumberField.mixedEmbedding.realSpace · cited by 87mixedEmbedding.realSpaceNumberField.mixedEmbedding.fundamentalCone.expMap_single · cited by 8fundamentalCone.expMap_si…OpenPartialHomeomorph.pi · cited by 6OpenPartialHomeomorph.pifundamentalCone.expMapCITED BYCITES

Cites8

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Cited by25

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