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Title:Compactly Generated Domain Theory
Authors: Matthias Schroeder ; Ingo Battenfeld ; Alex Simpson
Date: 2006
Publication Title:Mathematical Structures in Computer Science
Publication Type:Journal Article Publication Status:Published
Volume No:# 16(2) Page Nos:141-161
We propose compactly generated monotone convergence spaces as a well-behaved topological generalization of directed-complete partial orders (dcpos). The category of such spaces enjoys the usual properties of categories of ``predomains'' in denotational semantics. Moreover, such properties are retained if one restricts to spaces with a countable pseudobase in the sense of E.~Michael, a fact that permits connections to be made with computability theory, realizability semantics and recent work on the closure properties of topological quotients of countably based spaces (qcb spaces). We compare the standard domain-theoretic constructions of products and function spaces on dcpos with their compactly generated counterparts, showing that these agree in important cases though not in general.
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Bibtex format
author = { Matthias Schroeder and Ingo Battenfeld and Alex Simpson },
title = {Compactly Generated Domain Theory},
journal = {Mathematical Structures in Computer Science},
publisher = {CUP},
year = 2006,
volume = {# 16(2)},
pages = {141-161},

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