Editing Analytic continuation (section)

==Monodromy theorem==
{{Main|Monodromy theorem}}
The monodromy theorem gives a sufficient condition for the existence of a ''direct analytic continuation'' (i.e., an extension of an analytic function to an analytic function on a bigger set).

Suppose <math>D\subset \Complex</math> is an open set and ''f'' an analytic function on ''D''. If ''G'' is a [[simply connected]] [[Domain (mathematical analysis)|domain]] containing ''D'', such that ''f'' has an analytic continuation along every path in ''G'', starting from some fixed point ''a'' in ''D'', then ''f'' has a direct analytic continuation to ''G''.

In the above language this means that if ''G'' is a simply connected domain, and ''S'' is a sheaf whose set of base points contains ''G'', then there exists an analytic function ''f'' on ''G'' whose germs belong to ''S''.