Mathlib Map

Theorems · Definition · number theory

NumberField.mixedEmbedding.polarSpace

(K : Type u_1) → [Field K] → Type u_1

The space ℝ^(r₁+r₂) × ℝ^r₂, it is homeomorphic to the realMixedSpace, see homeoRealMixedSpacePolarSpace.

Defined in
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord
Cited by
17 results in Mathlib
Foundations
Depth 140 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.

NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace · cited by 11mixedEmbedding.homeoRealM…NumberField.mixedEmbedding.polarSpaceCoord · cited by 11mixedEmbedding.polarSpace…NumberField.mixedEmbedding.polarSpaceCoord_symm_apply · cited by 3mixedEmbedding.polarSpace…NumberField.mixedEmbedding.polarSpaceCoord_target · cited by 3mixedEmbedding.polarSpace…NumberField.mixedEmbedding.volume_preserving_homeoRealMixedSpacePolarSpace · cited by 2mixedEmbedding.volume_pre…NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_fst_ofIsComplex · cited by 2mixedEmbedding.homeoRealM…NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_fst_ofIsReal · cited by 2mixedEmbedding.homeoRealM…NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm · cited by 1mixedEmbedding.normAtComp…NumberField.mixedEmbedding.lintegral_comp_polarSpaceCoord_symm · cited by 1mixedEmbedding.lintegral_…NumberField.mixedEmbedding.volume_eq_two_pi_pow_mul_integral · cited by 1mixedEmbedding.volume_eq_…NumberField.mixedEmbedding.measurable_polarSpaceCoord_symm · cited by 1mixedEmbedding.measurable…NumberField.mixedEmbedding.polarSpaceCoord_target' · cited by 1mixedEmbedding.polarSpace…NumberField.mixedEmbedding.measurableEquivRealMixedSpacePolarSpace · cited by 0mixedEmbedding.measurable…NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply · cited by 0mixedEmbedding.homeoRealM…NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_snd · cited by 0mixedEmbedding.homeoRealM…Real · cited by 25697RealField · cited by 7404FieldNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceNumberField.InfinitePlace.IsComplex · cited by 272InfinitePlace.IsComplexmixedEmbedding.polarSpaceCITED BYCITES

Cites4

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

Cited by20

Results whose statement or proof uses this declaration.