Holomorphic branch
= Holomorphic branch
A single-valued choice from a multivalued relation which is a <holomorphic function> on its <domain>. For example, a <holomorphic branch> of the <square root> of a nonvanishing <holomorphic function> $h$ is a <holomorphic function> $g$ satisfying $g^2=h$. On a <domain>, any two such choices differ by a fixed sign, since their <continuous> quotient takes values in the <discrete set> $\{1,-1\}$.