Theorems · Definition · general topology
Circle.argEquiv
Circle ≃ ↑(Set.Ioc (-Real.pi) Real.pi)
Complex.arg and Circle.exp ∘ (↑) define an equivalence between Circle and (-π, π].
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 · cited by 25,697
- Equivstatement · cited by 8,337
- Set.Elemstatement · cited by 7,166
- Real.pistatement · cited by 1,774
- Set.Iocstatement · cited by 971
- Circlestatement and proof · cited by 227
- Complex.argproof · cited by 220
- Circle.expproof · cited by 73
- PartialEquiv.left_invproof · cited by 37
- Circle.argPartialEquivproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Circle.argEquiv_apply_coestatement and proof · cited by 0
- Circle.argEquiv_symm_applystatement and proof · cited by 0