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Problem 20

Suppose that \(J: \mathbb{C}_{\infty} \rightarrow \mathbb{C}_{\infty}\) is defined by \(J(z)=1 / z, z \in \mathbb{C}_{\infty} .\) Do our conventions imply \(J(0)=\infty\) and \(J(\infty)=\infty\) ? Does $$ \chi(J(z), J(w))=\chi(z, w) $$ hold in \(\mathbb{C}_{\infty} ?\)

Expert verified

The conventions imply \(J(0)=\infty\) and \(J(\infty)=0\), not \(\infty\). And \(\chi(J(z), J(w))\) is not equal to \(\chi(z, w)\) in the extended complex plane \(\mathbb{C}_{\infty}\).

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Chapter 2

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