Domain-representable spaces. (English summary) Fund. Math. 189 (2006), no. 3, 255–268.1730-6329 The authors investigate topological spaces that can be represented as the space of maximal elements of some continuous directed-complete partial order ( = domain) endowed with the Scott topology. They call these spaces domain representable and observe that domain representability can be thought of as a kind of topological completeness property related to Choquet-completeness. They establish that the Michael and Sorgenfrey lines are of this type, as is any subspace of a space of ordinals. They show that any completely regular T1-space is a closed subset of some domain representable space. They also prove that if X is domain representable, then so is any Gδ-subspace of X. From their study it follows that any Čech-complete space is domain representable. In particular their results answer questions of K. Martin. Finally they state that it would be interesting to know the extent to which various types of mappings preserve the property of domain representability
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