Theorems · Definition · complex analysis
Complex.equivRealProdCLM
ℂ ≃L[ℝ] ℝ × ℝ
The natural ContinuousLinearEquiv from ℂ to ℝ × ℝ.
- Defined in
- Mathlib.Analysis.Complex.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Complexstatement · cited by 5,565
- ContinuousLinearEquivstatement · cited by 743
- Real.sqrtproof · cited by 545
- Complex.equivRealProdLmproof · cited by 7
- Complex.equivRealProd_apply_le'proof · cited by 1
- LinearEquiv.toContinuousLinearEquivOfBoundsproof · cited by 0
Cited by14
Results whose statement or proof uses this declaration.
- Complex.polarCoordproof · cited by 26
- Complex.measurableEquivRealProdproof · cited by 11
- NumberField.mixedEmbedding.mixedSpaceToRealMixedSpaceproof · cited by 6
- Complex.frontier_reProdImproof · cited by 3
- Complex.polarCoord_symm_applyproof · cited by 3
- Complex.integral_boundary_rect_of_hasFDerivAt_real_off_countableproof · cited by 3
- Complex.closure_reProdImproof · cited by 2
- Complex.isHomeomorphicTrivialFiberBundle_improof · cited by 2
- Complex.isHomeomorphicTrivialFiberBundle_reproof · cited by 2
- Complex.equivRealProdCLM_symm_applystatement · cited by 1
- IsCompact.reProdImproof · cited by 0
- Complex.equivRealProdCLM_applystatement and proof · cited by 0