[CA] Extension of Holomorphic Functions

A type of function, defined by overconvergent power series, is lacunary function. For those overconvergent series, all the boundary points are not regular for the disc, i.e. the convergent disc is the natural domain of the function. We can check this by Ostrowski-Hadamard Theorem. Those are topics about holomorphic functions which can not be extended. There are also functions can be extended more but not trivial to find their natural domain. Plus, there are other topics in it, e.g. multiple branches for a function (like sqrt z and log z, etc.), homotopy vs singularity, as well as their connection, which is Monodromy Theorem.