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holomorphic function; Banach algebra; generator
Pseudoconvex domains are exhausted in such a way that we keep a part of the boundary fixed in all the domains of the exhaustion. This is used to solve a problem concerning whether the generators for the ideal of either the holomorphic functions continuous up to the boundary or the bounded holomorphic functions, vanishing at a point in $\mathbb{C}^{n}$ where the fibre is nontrivial, has to exceed $n$. This is shown not to be the case.
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