This is an exercise in Conway that I am stuck at. In fact I am surprised at this result. I cannot find a way to deal with the infinite points of $f$. Could anyone help me how to solve this exercise?
2026-03-25 12:55:05.1774443305
Meromorphic functions being continuous functions in the one point compactification of $C$
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If $(z_n)_{n\in\mathbb N}$ is a sequence of complex numbers which converges to $z_0$ and if $f$ has a pole at $z_0$, then $\lim_{n\to\infty}f(z_n)=\infty$ (this is a property of the poles). Therefore, $\tilde f$ is continuous at $z_0$. Since $\tilde f$ is also continuous at the non-poles of $f$, it is continuous everywhere.