A projective description of the space of holomorphic germs
type: Item
instance of: scholarly article
zbMATH Open document ID: 0990.46001
DOI: 10.1017/S0013091599000498
publication date: 2002-08-14T00:00:00Z
Mathematics Subject Classification ID: 46A13
Mathematics Subject Classification ID: 46F15
zbMATH DE Number: 1658546
zbMATH Keywords: projective description
zbMATH Keywords: Fréchet space
zbMATH Keywords: germs of holomorphic functions
zbMATH Keywords: inductive topology
zbMATH Keywords: compact-open topology
zbMATH Keywords: Taylor expansion
zbMATH Keywords: Taylor remainders
author: Pascal Laubin
MaRDI profile type: Publication
title: A projective description of the space of holomorphic germs
published in: Proceedings of the Edinburgh Mathematical Society. Series II
review text: For a compact set \(K\) in a complex Fréchet space denote by \({\mathcal O}(K)\) the space of germs of holomorphic functions on \(K\). Usually \({\mathcal O}(K)\) is endowed with the inductive topology with respect to all restriction maps \({\mathcal O}(\Omega)\to{\mathcal O}(K)\), where \(\Omega\) runs through all open neighborhoods of \(K\) and where \({\mathcal O}(\Omega)\) carries the compact-open topology. As main result the author shows that this topology can be described by an explicit system of semi-norms which are of Whitney type in the sense that are defined using the Taylor expansion as well as the Taylor remainders. The latter ones are not needed if \(K\) is locally connected. The results extend previous work of Mujica and of Rusek.
description: scientific article; zbMATH DE number 1658546