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Total Sets and Objects in Domain Theory
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Ulrich Berger
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**Abstract**

Total sets and objects generalizing total functions are introduced into
the theory of effective domains of Scott and Ersov. Using these
notions Kreisel's Density Theorem and the Theorem of
Kreisel-Lacombe-Shoenfield are generalized. As an immediate consequence
we obtain the well known continuity of computable functions on the
constructive reals as well as a domain theoretic characterization of the
Hereditarily Effective Operations.

**Bib entry**

@Article{Berger93, author = "Ulrich Berger", title = "Total Sets and Objects in Domain Theory", journal = "Annals of Pure and Applied Logic", year = "1993", volume = "60", pages = "91--117"}