Hello! I am reading a book on complex analysis and I came across this: If ##G \in \mathbb{C}## is a region, a function f is holomorphic in G and ##\gamma## is a piecewise smooth path with ##\gamma \sim_G 0## then ##\int_\gamma f = 0##. I want to make sure I understand. First of all, ##\gamma \sim_G 0## means that if G doesn't have "holes", any closed loop is homotopic to a point? And this also means that if G doesn't have holes, the integral of any holomorphic function over a closed loop is 0? Which means that in G any holomorphic function has an antiderivative? Thank you!(adsbygoogle = window.adsbygoogle || []).push({});

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# I Cauchy's Theorem

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