Topology, domain theory and theoretical computer science
type: Item
instance of: scholarly article
title: Topology, domain theory and theoretical computer science
zbMATH Open document ID: 0923.54027
DOI: 10.1016/S0166-8641(97)00222-8
author: Michael Mislove
published in: Topology and its Applications
publication date: 1999-10-19T00:00:00Z
review text: This article is an extended survey of the ways in which general topology, and more specifically the interconnections between topology and ordered sets, have played a fundamental role in the development of theoretical computer science. The author makes it clear that his attention in writing it was to `attract the attention of topologists to this area'; although the reviewer is not (by this definition) a topologist -- being already well aware of the developments in domain theory which form the central theme of this article -- he believes that the author has done an excellent job of expounding the material to those who have not met it before. In particular, the article provides a useful counterbalance to a recent one in the same journal by \textit{J. W. de Bakker} and \textit{E. P. de Vink} [Denotational models for programming languages: Application of Banach's fixed point theorem, ibid. 85, No. 1-3, 35-52 (1998)], which described the applications of complete metric spaces in denotational semantics, but underplayed the order-theoretical aspects of the subject.
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 06B35
Mathematics Subject Classification ID: 06F30
Mathematics Subject Classification ID: 68Q55
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 18B30
zbMATH DE Number: 1307934
zbMATH Keywords: extended survey
zbMATH Keywords: domain theory
zbMATH Keywords: complete metric spaces
zbMATH Keywords: denotational semantics
reviewed by: Peter Johnstone
MaRDI profile type: Publication
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