Editing Cauchy's integral theorem (section)

==== General formulation ====

Let <math>U \subseteq \Complex</math> be an [[open subset|open set]], and let <math>f: U \to \Complex</math> be a [[holomorphic function]]. Let <math>\gamma: [a,b] \to U</math> be a smooth closed curve. If  <math>\gamma</math> is [[Homotopy|homotopic]] to a constant curve, then:
<math display="block">\int_\gamma f(z)\,dz = 0. </math>where z є ''U''

(Recall that a curve is [[Homotopy|homotopic]] to a constant curve if there exists a smooth [[homotopy]] (within <math>U</math>) from the curve to the constant curve. Intuitively, this means that one can shrink the curve into a point without exiting the space.) The first version is a special case of this because on a [[Simply connected space|simply connected]] set, every closed curve is [[Homotopy|homotopic]] to a constant curve.