A non-topological view of dcpos as convergence spaces.
type: Item
instance of: scholarly article
title: A non-topological view of dcpos as convergence spaces.
zbMATH Open document ID: 1053.54018
DOI: 10.1016/S0304-3975(02)00706-5
author: Reinhold Heckmann
published in: Theoretical Computer Science
publication date: 2004-03-14T00:00:00Z
review text: The familiar embedding of the category \textbf{DCPO} of dcpos and Scott--continuous functions by means of the Scott topology lacks some desirable properties: It does not preserve products, binary joins are not always continuous in the proper topological sense, and pointwise joins of continuous functions \(X\rightarrow L_c\) may fail to be continuous. The author constructs an embedding \(D\) from \textbf{DCPO} into the category \textbf{CONV} of convergence spaces that is free from the above deficiencies. Moreover he demonstrates that the convergence spaces appearing in the image of \(D\), which he calls \textit{cotopological dcpos}, enjoy many interesting properties familiar from continuous dcpos and behave rather well with respect to the formations of function spaces. For a dcpo \(D\), its topological structure agrees with its cotopological convergence structure if and only if \(D\) is a continuous dcpo.
reviewed by: Horst Herrlich
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 06B35
Mathematics Subject Classification ID: 54A05
zbMATH DE Number: 2055972
zbMATH Keywords: domains
zbMATH Keywords: topology
zbMATH Keywords: convergence space
zbMATH Keywords: function space
MaRDI profile type: Publication
cites work: Equilogical spaces
cites work: Q4098335
cites work: Q3940471
cites work: On \(d\)-spaces
cites work: Q3898534
cites work: Q4373421
cites work: Q4218936
cites work: Quantitative semantics, topology, and possibility measures
cites work: Cartesian Closed Topological Hulls
cites work: Q3866268
cites work: Filter spaces and continuous functionals
cites work: Completion of a Construction of Johnstone
cites work: Q4104538
cites work: Q3732529
cites work: Q3940470
cites work: Q4064668
cites work: Q3949664
description: scientific article; zbMATH DE number 2055972