Why do we require the (whole) domain to be simply connected in Cauchy's theorem, residue theorem, etc.? – math.stackexchange.com

Why do we require the (whole) domain to be simply connected in Cauchy's theorem, residue theorem, etc.? – math.stackexchange.com

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Main Question A very common form of Cauchy's integral theorem is Let $A\subset\mathbf{C}$ be simply connected and open, $f:A\rightarrow\mathbf{C}$ analytic, $I$ a compact interval, and $\gamma:I\...

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