Topology Proceedings 30 No. 1 (2006), pp. 83-93

A Countably-Based Domain Representation of a Non-Regular Hausdorff Space

Harold Bennett and David Lutzer

In this paper, we give an example of a countably-based 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.

Keywords: domain, domain-representable space, countably-based domain, Hausdorff but not regular

Mathematics Subject Classification: 54H99 (06B35 06B30 54D80)

Document formats: PDF file 193.4 Kb

Topology Proceedings, Volume 30, No. 1 (2006)
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