Theorems · Definition · real analysis
polarCoord
OpenPartialHomeomorph (ℝ × ℝ) (ℝ × ℝ)
The polar coordinates are an open partial homeomorphism in ℝ^2, mapping (r cos θ, r sin θ)
to (r, θ). It is a homeomorphism between ℝ^2 - (-∞, 0] and (0, +∞) × (-π, π).
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Set.ofPredproof · cited by 6,101
- Equiv.symmproof · cited by 3,681
- Real.piproof · cited by 1,774
- SProd.sprodproof · cited by 1,750
- Set.Ioiproof · cited by 1,463
- Set.Iooproof · cited by 1,214
- OpenPartialHomeomorphstatement · cited by 664
- Real.sqrtproof · cited by 545
- Real.cosproof · cited by 424
- Real.sinproof · cited by 389
Cited by27
Results whose statement or proof uses this declaration.
- Complex.polarCoordproof · cited by 26
- NumberField.mixedEmbedding.polarCoordRealproof · cited by 13
- pi_polarCoord_symm_target_ae_eq_univstatement and proof · cited by 3
- hasFDerivAt_pi_polarCoord_symmstatement and proof · cited by 3
- hasFDerivAt_polarCoord_symmstatement and proof · cited by 3
- polarCoord_source_ae_eq_univstatement and proof · cited by 3
- Complex.polarCoord_symm_applyproof · cited by 3
- integral_comp_polarCoord_symmstatement and proof · cited by 2
- NumberField.mixedEmbedding.polarCoordReal_symm_target_ae_eq_univproof · cited by 2
- Complex.integral_comp_polarCoord_symmstatement and proof · cited by 2
- integral_gaussian_sq_complexproof · cited by 2
- abs_fst_of_mem_pi_polarCoord_targetstatement and proof · cited by 2