Theorems · Theorem · complex analysis
Complex.continuousOn_one_add_mul_inv
∀ {z : ℂ}, 1 + z ∈ Complex.slitPlane → ContinuousOn (fun t => (1 + t • z)⁻¹) (Set.Icc 0 1)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 171 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.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Set.Iccstatement and proof · cited by 1,702
- ContinuousOnstatement · cited by 1,411
- Complex.slitPlanestatement and proof · cited by 113
- continuousOn_id'proof · cited by 109
- continuousOn_constproof · cited by 96
- ContinuousOn.inv₀proof · cited by 13
- ContinuousOn.fun_smulproof · cited by 9
- Complex.slitPlane_ne_zeroproof · cited by 8
- ContinuousOn.const_addproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- Complex.norm_log_sub_logTaylor_leproof · cited by 4
- Complex.log_eq_integralproof · cited by 1
- Complex.integrable_pow_mul_norm_one_add_mul_invproof · cited by 0