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Title:Compactly generated domain theory
Authors: Alexander Simpson ; Ingo Battenfeld ; Matthias Schroeder
Date:Apr 2006
Publication Title:Compactly generated domain theory
Publisher:Cambridge University Press
Publication Type:Journal Article Publication Status:Published
Volume No:16 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 = { Alexander Simpson and Ingo Battenfeld and Matthias Schroeder },
title = {Compactly generated domain theory},
journal = {Compactly generated domain theory},
publisher = {Cambridge University Press},
year = 2006,
month = {Apr},
volume = {16},
pages = {141-161},
doi = {10.1017/S0960129506005202},

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