## Algebras of Holomorphic Functions: 40 Lectures, Parts 1-7 |

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### Contents

Homomorphism Spaces of Stable Algebras | 1 |

Differentiably Stable Algebras on Compact Sets 2 2 | 22 |

Stable Uniform Algebras | 38 |

4 other sections not shown

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### Common terms and phrases

AA(U AH(X algebra of holomorphic AM(X analytic function algebra approximation Bishop's Theorem Cauchy filter Chapter choose compact holomorphic compact holomorphicly convex compact neighborhood compact set compact subset complex analytic manifold component contradiction convergence on compact Corollary countable denote differentiably stable analytic domain of holomorphy f e Hol(U fundamental system Hence Hol(M Hol(V Hol(W holomorphic functions holomorphic set holomorphicly convex set homomorphism space inductive limit topology intersection Lemma manifold spread Mer(X meromorphic one-one open neighborhood open set open subset Poly Poly-hull(X polydisc polyhedra polynomial polynomial F proof of Theorem proper map properties Rat-hull(X rational relatively compact Serre duality set containing special holomorphic polyhedron stable analytic algebra stable uniform algebra Stein manifold submanifold subset of Cn subvariety supp Suppose system of neighborhoods uniform convergence unit polynomial weak peak point zero dimensional