Domain-representability of certain complete spaces

Harold Bennett, David Lutzer

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

In this paper we show that three major classes of topological spaces are domain-representable, 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 α- favorable spaces (with stationary strategies) that have either a G δ-diagonal or a base of countable order, and (iii) complete quasi-developable T3-spaces. It follows that any regular space with a monotonically complete base of countable order (in the sense of Wicke and Worrell) is domain-representable, 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 a-favorable spaces (with stationary strategies) that have a Gδ-diagonal can be used to show that spaces such as the Sorgenfrey line, the Michael line, the Moore plane, the Nagata plane, and Heath's V-space are domain-representable, and to show that a domain-representable space can be Hausdorff but not regular.

Original languageEnglish
Pages (from-to)753-772
Number of pages20
JournalHouston Journal of Mathematics
Volume34
Issue number3
StatePublished - 2008

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