Compactly generated domain theory

@article{Battenfeld2006CompactlyGD,
  title={Compactly generated domain theory},
  author={Ingo Battenfeld and Matthias Schr{\"o}der and Alex K. Simpson},
  journal={Mathematical Structures in Computer Science},
  year={2006},
  volume={16},
  pages={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… CONTINUE READING
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