# Clarification of Cauchy-Goursat Theorem

Cauchy-Goursat: If $f$ is analytic in a simply connected domain D, then $\int_{c}f(z) dz=0$ for any closed curve $c$ in D.

However, I have seen questions where Cauchy-Goursat has been used when the function is just analytic in and on a closed curve C. Where are the simply connected regions in these situations? I know that Cauchy Gourmet can be applied to curves within C but why is it possible on C itself?

• The key is any closed curve. – Jacky Chong Apr 2 '18 at 3:35
• Yes but it is a closed curve in D. How about the boundary of D? Is C itself in any simply connected region? If so it that region determined by the open balls wise centers are points n the curve? – Jhon Doe Apr 2 '18 at 3:39