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Nonclassical Techniques for Models of Computation
 Topology Proceedings
, 1999
"... After surveying recent work and new techniques in domain theoretic models of spaces, we introduce a new topological concept called recurrence, and consider some of its applications to the model problem. ..."
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Cited by 9 (4 self)
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After surveying recent work and new techniques in domain theoretic models of spaces, we introduce a new topological concept called recurrence, and consider some of its applications to the model problem.
The Space of Maximal Elements in a Compact Domain
, 2001
"... In this paper we try to improve the current state of understanding concerning models of spaces with Scott domains. The main result given is that any developable space which has a model by a Scott domain must be Cechcomplete. An important consequence is that any metric space homeomorphic to the max ..."
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Cited by 6 (3 self)
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In this paper we try to improve the current state of understanding concerning models of spaces with Scott domains. The main result given is that any developable space which has a model by a Scott domain must be Cechcomplete. An important consequence is that any metric space homeomorphic to the maximal elements of a Scott domain must be completely metrizable. 1
A CountablyBased Domain Representation of a NonRegular Hausdorff Space
, 2006
"... In this paper we give an example of a countablybased algebraic domain D such that max(D) is Hausdorff but not regular in the relative Scott topology, and such that max(D) contains the usual space of rational numbers as a closed subspace. Our example shows that certain known results about max(D), wh ..."
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Cited by 2 (0 self)
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In this paper we give an example of a countablybased algebraic domain D such that max(D) is Hausdorff but not regular in the relative Scott topology, and such that max(D) contains the usual space of rational numbers as a closed subspace. Our example shows that certain known results about max(D), where max(D) is regular and D is countably based, are the sharpest possible. MR Classifications: primary = 54H99;secondary = 06B35, 06B30, 54D80 1
Abstract How Do Domains Model Topologies?
"... In this brief study we explicitly match the properties of spaces modelled by domains with the structure of their models. We claim that each property of the modelled topology is coupled with some construct in the model. Examples are pairs: (i) firstcountability strictly monotone map, (ii) developabi ..."
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In this brief study we explicitly match the properties of spaces modelled by domains with the structure of their models. We claim that each property of the modelled topology is coupled with some construct in the model. Examples are pairs: (i) firstcountability strictly monotone map, (ii) developability measurement, (iii) metrizability partial metric, (iv) ultrametrizability tree, (v) Choquetcompletenessdcpo, and more. By making this correspondence precise and explicit we reveal how domains model topologies. 1