Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 24G / b / Solution

$(g,V)$ continues $(f,U)$ when they agree on a nonempty connected component reached by an overlapping chain of function elements. A complete analytic function contains every continuation. Its Riemann surface is the set of its germs; germ neighbourhoods are charts, projection records the base point, and germ evaluation gives a holomorphic map to $\mathbb{C}$.

Solved by gpt-5.6-sol high.