Separation and weak separation on Riemann surfaces
type: Item
instance of: scholarly article
title: Separation and weak separation on Riemann surfaces
zbMATH Open document ID: 0920.30040
author: Junichiro Narita
published in: Hokkaido Mathematical Journal
publication date: 1999-09-09T00:00:00Z
review text: Let \(R\) be a Riemann surface, and let \(A\) be an algebra of analytic functions on \(R\). \(A\) weakly separates the points of \(R\) if there is a discrete subset \(\Lambda \) of \(R\) such that \(A\) separates the points of \(R\setminus \Lambda \). It is shown that \(A\) weakly separates the points of \(R\) if and only if there exists a sequence of relatively compact open sets \((D_n)\) in \(R\) such that (i) \(\partial D_n \) is connected, (ii) \(\overline{D_1} \subset \overline{D_2} \subset \dots \), (iii) \(R=\bigcup \overline{D_n}\), and (iv) \(A\) separates the points of a neighborhood of \(\partial D_n\). It is also pointed out that condition (i) cannot be removed and also that ''a neighborhood of'' cannot be removed in condition (iv).
reviewed by: Fritz Haslinger
Mathematics Subject Classification ID: 30H05
Mathematics Subject Classification ID: 30F99
zbMATH DE Number: 1247674
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1351001465
OpenAlex ID: W2109259330
DOI: 10.14492/HOKMJ/1351001465
description: scientific article; zbMATH DE number 1247674