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Dynamics in One Complex Variable. (AM-160), 3rd Edition by John Milnor

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§1. Simply Connected Surfaces

The first three sections will present an overview of some background material.

If Vimage is an open set of complex numbers, a function f : Vimage is called holomorphic (or “complex analytic”) if the first derivative

image

is defined and continuous as a function from V to image, or equivalently if f has a power series expansion about any ...

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