An extension theorem for sober spaces and the Goldman topology
type: Item
instance of: scholarly article
title: An extension theorem for sober spaces and the Goldman topology
zbMATH Open document ID: 1042.54003
DOI: 10.1155/S0161171203212230
author: Ezzeddine Bouacida
author: Othman Echi
author: Gabriel Picavet
author: Ezzeddine Salhi
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-12-03T00:00:00Z
full work available at URL: https://eudml.org/doc/50863
review text: Goldman points of a topological space are defined in order to extend the notion of prime \(G\)-ideals of a ring. We associate to any topological space a new topology called Goldman topology. For sober spaces, we prove an extension theorem of continuous maps. As an application, we give a topological characterization of the Jacobson subspace of the spectrum of a commutative ring. Many examples are provided to illustrate the theory.
reviewed by: Bernhard Behrens
Mathematics Subject Classification ID: 54A10
Mathematics Subject Classification ID: 54B35
Mathematics Subject Classification ID: 54F65
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 2012613
zbMATH Keywords: sober space
zbMATH Keywords: quasihomeomorphism extension
zbMATH Keywords: prime spectrum
zbMATH Keywords: spectral space
zbMATH Keywords: Goldman point
zbMATH Keywords: Goldman topology
zbMATH Keywords: Jacobson space
zbMATH Keywords: Noetherian space
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2012613