Let $A,B$ denote domains in $\mathbb{C}$, and $f:A\rightarrow B$ is a holomorphic mapping. Suppose that $f$ is proper ($f^{-1}$ takes compact sets to compact sets). Prove that $f(A)=B.$
Proper Holomorphic Mappings
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complex-analysis
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0$f$ must be non-constant... – 2011-08-23