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2tti abelian groups algebra analytic sheaf associated sheaf called the sheaf Cauchy-Riemann equation coefficients compact set compact subset Complex Analysis complex valued function complex variable component connected continuous function converges Corollary Definition denote df(p differential disc divisor domain of holomorphy dzAdz f and g f e Hol(ft f e Hol(U follows function f global Hence Hol(D Hol(U)-hull holomor holomorphic functions Hq(U implies lemma Leray cover Let f e locally finitely maximum modulus meromorphic function modulus theorem Noetherian one-one open neighborhood open set open subset p e ft phic functions pole of order polydisc power series presheaf Proof prove Reinhardt domain Remark Runge's theorem sequence of sheaves sheaf of germs sheaves of abelian subharmonic topology unique uu is open vector Weierstrass polynomial Weierstrass preparation theorem zn(p