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

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. MR Classifications: primary = 54H99;secondary = 06B35, 06B30, 54D80

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