Theorems · Definition · general topology
AddCircle.toCircle
{T : ℝ} → AddCircle T → CircleThe canonical map fun x => exp (2 π i x / T) from ℝ / ℤ • T to the unit circle in ℂ.
If T = 0 we understand this as the constant function 1.
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Circlestatement · cited by 227
- AddCirclestatement · cited by 189
- Function.Periodic.liftproof · cited by 7
- AddCircle.scaled_exp_map_periodicproof · cited by 6
Cited by45
Results whose statement or proof uses this declaration.
- fourierproof · cited by 62
- AddCircle.toCircle_zerostatement and proof · cited by 9
- Polynomial.toAddCircleproof · cited by 9
- AddChar.zmodproof · cited by 7
- fourier_applystatement · cited by 7
- fourier_coe_applyproof · cited by 7
- fourier_zeroproof · cited by 5
- AddCircle.injective_toCirclestatement and proof · cited by 4
- AddCircle.toCircle_addstatement · cited by 4
- Complex.tsum_exp_neg_quadraticproof · cited by 3
- orthonormal_fourierproof · cited by 3
- fourier_addproof · cited by 3