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 $\{1,-1\}$.