By an analytic isomorphism of $\Omega$, I mean an analytic function $\Omega \to \Omega$, with an analytic inverse.
What are the analytic isomorphisms of $\Omega = \mathbb{C} \setminus \{p_1,\ldots,p_n\}$?
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complex-analysis
analyticity
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4Can you extend the function to the whole sphere by continuity? – 2012-10-22
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0@MarianoSuárez-Alvarez Thanks. You mean I should look at analytic isomorphisms of the sphere (that is Mobius transformations), that preserve the set $\{p_1,\ldots,p_n \}$. – 2012-10-22