Function element
= Function element
A function element is a pair $(f,D)$ consisting of a nonempty disk and a <holomorphic function> on that disk. Its local value determines a <germ of a holomorphic function>. Elements agreeing on an overlapping neighborhood continue one another; chains of such continuations produce the <complete analytic function> generated by an element. An algebraic identity holding in one element persists along any continuation chain by the <identity theorem>.