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PARTS AND ANALYTIC STRUCTURE FOR 3PX
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alge algebra-homomorphism analytic structure Banach function algebra basis of holomorphically belongs boun closed analytic polyhedron closed subset commutative compact set compact space compact subset complex analytic subvariety complex plane complex-extreme point Consequently continuous map coordinates Cousin I problem dary denoted domain equicontinuous exist a neighbourhood exists a function f is holomorphic following theorem function algebra jf function f gebra Gelfand representation Gleason Hausdorff space hemicompact Hence holomor holomorphic functions holomorphic in neighbourhoods holomorphically convex sets homeomorphism intersection irreducible JP(X lemma Let f locally m-convex algebra maximum modulus principle maximum modulus theorem maximum principle minimal peakset morphic natural number neighbourhood basis neighbourhood N(x open set points of V(x polydisc positive number prove semisimple separates the points spectrum spread map Stein manifold strong boundary point subset of Cn Suppose there exist tion algebra topology of uniform U0nU uniform convergence unit disc weak topology wordt