Spaces modelled by an algebra on \([0,\infty ]\) and their complete objects
type: Item
instance of: scholarly article
title: Spaces modelled by an algebra on \([0,\infty ]\) and their complete objects
zbMATH Open document ID: 1214.18001
published in: Topology and its Applications
publication date: 2010-05-19T00:00:00Z
review text: The authors investigate constructs of affine sets over \([0,\infty]\) that are defined by means of a given algebra structure on \([0, \infty]\), endowed with the Zariski closure operator. They establish a duality theory and characterize the complete objects. Moreover, they demonstrate that various familiar constructs fit into this setting, in particular approach spaces, pseudometric spaces, topological spaces and non-Archimedean spaces.
reviewed by: Horst Herrlich
Mathematics Subject Classification ID: 18A10
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 54B30
zbMATH DE Number: 5710124
zbMATH Keywords: affine object
zbMATH Keywords: Zariski closure
zbMATH Keywords: complete object
zbMATH Keywords: approach space
zbMATH Keywords: topological space
zbMATH Keywords: non-Archimedean space
author: Eva Colebunders
author: Eraldo Giuli
author: Robert Lowen
MaRDI profile type: Publication
full work available at URL: j.topol.2009.05.016
OpenAlex ID: W2077494204
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DOI: 10.1016/J.TOPOL.2009.05.016
description: scientific article; zbMATH DE number 5710124