A function element is a pair 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.

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  1. Germ of a holomorphic function
  2. Riemann surfaces
  3. Complex analysis
  4. Analysis
  5. Area of mathematics
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