Ideal models of spaces. (English) Zbl 1044.54005
This paper is a continuation of the author’s programme of studying when spaces can be ‘modelled’ by representing them as the subspaces of maximal points of continuous posets equipped with the Scott topology. In the present paper he considers ‘ideal dcpo’s’ in which every element is either compact or maximal. The main result asserts that if \(D\) is an ideal domain with \(\max(D)\) metrizable, then \(\max(D)\) is a \(G_{\delta}\) subset of \(D\). As a consequence he obtains a remarkable characterization of completely metrizable spaces, as those metrizable spaces which have ideal models.
Reviewer: Peter T. Johnstone (Cambridge)
MSC:
| 54B99 | Basic constructions in general topology |
| 54F65 | Topological characterizations of particular spaces |
| 06B30 | Topological lattices |
| 54E35 | Metric spaces, metrizability |
| 68Q55 | Semantics in the theory of computing |
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