Let $f,g$ be a pair of univalent functions on a proper subdomain $\Omega$ of $\mathbb C$. Does their sum $f+g$ necessarily omit any complex value? Similarly, can all holomorphic function be written as sums of univalent functions?

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`$z$`

and`$1/z$`

on`${\bf C} - \{0\}$`

. – Nik Weaver Jun 16 '12 at 0:42