## Functions of one complex variable |

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### Contents

1 The real numbers | 1 |

Metric Spaces and the Topology of C | 11 |

Elementary Properties and Examples of Analytic Functions | 30 |

Copyright | |

41 other sections not shown

### Common terms and phrases

analytic continuation analytic function analytic in G assume bounded Cauchy sequence Cauchy's Theorem circle closed curve closed rectifiable curve compact subset complete analytic function complex number component contains a disk continuous function convex Corollary curve in G Definition diam differentiable disk of radius entire function equation essential singularity Exercise fact finite number follows formula function element function f function on G g is analytic gives harmonic function Hence homeomorphism homotopic If/is implies integer Lemma Let f Let G lim sup limit point logarithm meromorphic function metric space Mobius transformation never vanishes one-one open set open subset path point in G point x0 pole polynomial properties Proposition prove radius of convergence rational function reader real number region G removable singularity result satisfies simply connected simply connected region subharmonic subset of G suppose that/(z that/is topological space uniformly continuous zero