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Topological Games in Domain Theory
 Topology Appl
"... We prove that a metric space may be realized as the set of maximal elements in a continuous dcpo if and only if it is completely metrizable by showing more generally that the space of maximal elements in a domain is always complete in a sense rst introduced by Choquet. ..."
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Cited by 11 (0 self)
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We prove that a metric space may be realized as the set of maximal elements in a continuous dcpo if and only if it is completely metrizable by showing more generally that the space of maximal elements in a domain is always complete in a sense rst introduced by Choquet.
Domain representability of certain complete spaces
 Houston J. Math
"... Abstract. In this paper we show that three major classes of topological spaces are domainrepresentable, i.e., homeomorphic to the space of maximal elements of some domain (=continuous dcpo) with the relative Scott topology. The three classes are: (i) T3 subcompact spaces, (ii) strongly αfavorable ..."
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Cited by 8 (3 self)
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Abstract. In this paper we show that three major classes of topological spaces are domainrepresentable, i.e., homeomorphic to the space of maximal elements of some domain (=continuous dcpo) with the relative Scott topology. The three classes are: (i) T3 subcompact spaces, (ii) strongly αfavorable spaces (with stationary strategies) that have either a Gδdiagonal or a base of countable order, and (iii) complete quasidevelopable T3spaces. It follows that any regular space with a monotonically complete base of countable order (in the sense of Wicke and Worrell) is domainrepresentable, as is any space with exactly one limit point. (In fact, any space with exactly one limit point is domain representable using a Scott domain.) The result on strongly αfavorable spaces (with stationary strategies) that have a Gδdiagonal can be used to show that spaces such as the Sorgenfrey line, the Michael line, the Moore plane, the Nagata plane, and Heath’s Vspace are domainrepresentable, and to show that a domainrepresentable space can be Hausdorff but not regular. 1.
Ideal Models of Spaces
 Theoretical Computer Science
, 2000
"... Ideal domains have an elementary order theoretic structure: Every element is either compact or maximal. Despite this, we establish that (1) They can model any space currently known to possess a countably based model, and (2) The metric spaces with ideal models are exactly the completely metrizab ..."
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Cited by 5 (2 self)
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Ideal domains have an elementary order theoretic structure: Every element is either compact or maximal. Despite this, we establish that (1) They can model any space currently known to possess a countably based model, and (2) The metric spaces with ideal models are exactly the completely metrizable spaces.
The Regular Spaces With Countably Based Models
 THEORETICAL COMPUTER SCIENCE
"... The regular spaces which may be realized as the set of maximal elements in an !continuous dcpo are the Polish spaces. In addition, we give a new and conceptually simple model for complete metric spaces. These results enable ..."
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Cited by 4 (2 self)
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The regular spaces which may be realized as the set of maximal elements in an !continuous dcpo are the Polish spaces. In addition, we give a new and conceptually simple model for complete metric spaces. These results enable
LINEARLY ORDERED TOPOLOGICAL SPACES AND WEAK DOMAIN REPRESENTABILITY
"... Abstract. It is well known that domain representable spaces, that is topological spaces that are homeomorphic to the space of maximal elements of some domain, must be Baire. In this paper it is shown that every linearly ordered topological space (LOTS) is homeomorphic to an open dense subset of a we ..."
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Abstract. It is well known that domain representable spaces, that is topological spaces that are homeomorphic to the space of maximal elements of some domain, must be Baire. In this paper it is shown that every linearly ordered topological space (LOTS) is homeomorphic to an open dense subset of a weak domain representable space. This means that weak domain representable spaces need not be Baire. 1.
Domain Representability and the Choquet Game in Moore and BCOspaces
, 2007
"... Abstract: In this paper we investigate the role of domain representability and Scottdomain representability in the class of Moore spaces and the larger class of spaces with a base of countable order. We show, for example, that in a Moore space, the following are equivalent: domain representability ..."
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Abstract: In this paper we investigate the role of domain representability and Scottdomain representability in the class of Moore spaces and the larger class of spaces with a base of countable order. We show, for example, that in a Moore space, the following are equivalent: domain representability; subcompactness; the existence of a winning strategy for player α ( = the nonempty player) in the strong Choquet game Ch(X); the existence of a stationary winning strategy for player α inCh(X); and Rudin completeness. We note that a metacompact Čechcomplete Moore space described by Tall is not Scottdomain representable and also give an example of Čechcomplete separable Moore space that is not cocompact and hence not Scottdomain representable. We conclude with a list of open questions.