Theorems · Theorem · complex analysis
Complex.mem_slitPlane_of_norm_lt_one
∀ {z : ℂ}, ‖z‖ < 1 → 1 + z ∈ Complex.slitPlaneThe slit plane includes the open unit ball of radius 1 around 1.
- Defined in
- Mathlib.Analysis.Complex.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Complex.slitPlanestatement · cited by 113
- dist_self_add_leftproof · cited by 11
- Complex.ball_one_subset_slitPlaneproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Complex.norm_log_sub_logTaylor_leproof · cited by 4
- Complex.one_add_cpow_hasFPowerSeriesOnBall_zeroproof · cited by 3
- Complex.hasSum_arctan_auxproof · cited by 1
- Complex.norm_log_one_sub_inv_add_logTaylor_neg_leproof · cited by 1
- Complex.integrable_pow_mul_norm_one_add_mul_invproof · cited by 0