MATHEMATICA BOHEMICA, Vol. 133, No. 2, pp. 121-131, 2008

# Trivial generators for nontrivial fibres

## Linus Carlsson

Linus Carlsson, Department of Mathematics and Mathematical Statistics, Umea University, S-901 87 Umea, Sweden, e-mail: linus@math.umu.se

Abstract: 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.

Keywords: holomorphic function, Banach algebra, generator

Classification (MSC 2000): 32A65, 32W05, 46J20

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