Runge exhaustions of domains in \({\mathbb{C}}^ n\)
type: Item
instance of: scholarly article
title: Runge exhaustions of domains in \({\mathbb{C}}^ n\)
zbMATH Open document ID: 0618.32013
DOI: 10.1007/BF01168001
author: Bill Zame
author: J. E. Fornæss
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173811
review text: A domain \(D\subset {\mathbb{C}}^ n\) is said to have Runge exhaustion if for every compact \(K\subset D\) there exists an open set \(U\subset \subset D\) with \(K\subset U\) such that for every holomorphic function f on U and every compact set \(F\subset U\) there exists a sequence of holomorphic functions on D converging uniformly to f on F. - A domain is constructed in \({\mathbb{C}}^ 2\) with no Runge exhaustion.
Mathematics Subject Classification ID: 32E30
zbMATH DE Number: 4002500
zbMATH Keywords: no Runge exhaustion
MaRDI profile type: Publication
cites work: Spreading Polydiscs on Complex Manifolds
cites work: Uniform Approximation on Compact Sets in $\mathsf{C}^n$.
cites work: On Serre Duality and Envelopes of Holomorphy
OpenAlex ID: W1589524064
description: scientific article; zbMATH DE number 4002500