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Preliminary Concepts 1 Sets and Functions
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absolutely convergent analytic angle apply assertion boundary bounded called Cauchy Cauchy's circle circloid cluster point complex numbers component conclude conformal equivalence conformal mapping consider contains continuous function corresponding curve defined definition denote Dirichlet problem disk domain element endpoints entire function equation essential singularity Exercise exists fact finite number follows formula function f geometric harmonic functions hence holomorphic function implies infinite integral inverse Lemma lim sup limit point mapping metric space Mobius transformation notation open set parametric representation pole polygon polynomial positively oriented power series proof of Theorem Prove reader real axis real numbers removable singularity result Riemann surface satisfies Section sequence Show simple closed simply connected simply connected region subarc sufficiently Suppose triangle uniform convergence uniformly unique valid zero