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Tag Archives: Cauchy’s theorem
Homotopy version of Cauchy’s theorem
Let $\gamma_0$ and $\gamma_1$ be piecewise smooth curves defined on the interval $[a, b]$ with the same end points, i.e., $\gamma_0(a) = \gamma_1(a)$ and $\gamma_0(b) = \gamma_1(b)$. If $U \subset \mathbb{C}$ is an open set, then $\gamma_0$ and $\gamma_1$ are … Continue reading