Theorems · Definition · number theory
NumberField.mixedEmbedding.mixedSpaceToRealMixedSpace
(K : Type u_1) → [inst : Field K] → NumberField.mixedEmbedding.mixedSpace K ≃ₜ NumberField.mixedEmbedding.realMixedSpace K
The natural homeomorphism between the mixed space ℝ^r₁ × ℂ^r₂ and the real mixed space
ℝ^r₁ × (ℝ × ℝ)^r₂.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 164 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- Complexstatement · cited by 5,565
- Homeomorphstatement · cited by 725
- 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
- ContinuousLinearEquiv.toHomeomorphproof · cited by 44
- NumberField.mixedEmbedding.realMixedSpacestatement · cited by 34
- Homeomorph.reflproof · cited by 25
- Complex.equivRealProdCLMproof · cited by 11
Cited by6
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.polarCoord_symm_eqstatement · cited by 3
- NumberField.mixedEmbedding.volume_preserving_mixedSpaceToRealMixedSpace_symmstatement · cited by 2
- NumberField.mixedEmbedding.lintegral_comp_polarCoord_symmproof · cited by 1
- NumberField.mixedEmbedding.integral_comp_polarCoord_symmproof · cited by 1
- NumberField.mixedEmbedding.measurable_polarCoord_symmproof · cited by 1
- NumberField.mixedEmbedding.mixedSpaceToRealMixedSpace_applystatement · cited by 0