Compactly Generated Domain Theory

Ingo Battenfeld, Matthias Schröder, Alexander Simpson

Research output: Contribution to journalArticlepeer-review


We propose compactly generated monotone convergence spaces as a well-behaved topological generalisation 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.
Original languageEnglish
Pages (from-to)141-161
Number of pages21
JournalMathematical Structures in Computer Science
Issue number2
Publication statusPublished - 2006


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