Theorems · Definition · complex analysis
Complex.slitPlane
Set ℂ
The slit plane is the complex plane with the closed negative real axis removed.
- Defined in
- Mathlib.Analysis.Complex.Basic
- Cited by
- 113 results in Mathlib
- Foundations
- Depth 90 from the axioms, rests on 1,953 definitions · 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.
- Setstatement · cited by 53,352
- Set.ofPredproof · cited by 6,101
- Complexstatement and proof · cited by 5,565
- Complex.reproof · cited by 882
- Complex.improof · cited by 591
Cited by114
Results whose statement or proof uses this declaration.
- Complex.hasStrictDerivAt_logstatement and proof · cited by 8
- Complex.ofReal_mem_slitPlanestatement · cited by 8
- Complex.slitPlane_ne_zerostatement and proof · cited by 8
- analyticAt_clogstatement and proof · cited by 6
- Complex.hasStrictDerivAt_cpow_conststatement and proof · cited by 5
- Complex.mem_slitPlane_of_norm_lt_onestatement · cited by 5
- HasDerivAt.cpow_conststatement and proof · cited by 5
- Complex.hasDerivAt_logstatement and proof · cited by 4
- AnalyticAt.harmonicAt_log_normproof · cited by 4
- continuousAt_cpowstatement and proof · cited by 4
- Complex.mem_slitPlane_iffstatement · cited by 4
- Complex.hasDerivAt_sqrtstatement and proof · cited by 3