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Theorems · Definition · complex analysis

Complex.expPartialHomeomorph

Deprecated since 2026-01-13Use Complex.expOpenPartialHomeomorph instead.

OpenPartialHomeomorph ℂ ℂ

Alias of Complex.expOpenPartialHomeomorph. Complex.exp as an OpenPartialHomeomorph with source = {z | -π < im z < π} and target = {z | 0 < re z} ∪ {z | im z ≠ 0} (a.k.a. slitPlane). This definition is used to prove that Complex.log is complex differentiable at all points but the negative real semi-axis.

Defined in
Mathlib.Analysis.SpecialFunctions.Complex.Log
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Foundations
Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
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Complex · cited by 5565ComplexOpenPartialHomeomorph · cited by 664OpenPartialHomeomorphComplex.expOpenPartialHomeomorph · cited by 2Complex.expOpenPartialHom…Complex.expPartialHomeomorphCITED BYCITES

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