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Title: Lattices of Scott-closed sets
Authors: Ho, Weng Kin
Zhao, Dongsheng
Keywords: Domain
Complete semilattice,
Scott-closed set
C-continuous lattice
C-algebraic lattice
Issue Date: 2009
Citation: Ho, W. K., & Zhao, D. (2009). Lattices of Scott-closed sets. Comment. Math. Univ. Carolin., 50(2), 297-314.
Abstract: A dcpo P is continuous if and only if the lattice C(P) of all Scott- closed subsets of P is completely distributive. However, in the case where P is a non-continuous dcpo, little is known about the order structure of C(P). In this paper, we study the order-theoretic properties of C(P) for general dcpo's P. The main results are: (i) every C(P) is C-continuous; (ii) a complete lattice L is isomorphic to C(P) for a complete semilattice P if and only if L is weak-stably C-algebraic; (iii) for any two complete semilattices P and Q, P and Q are isomorphic if and only if C(P) and C(Q) are isomorphic. In addition, we extend the function P 7! C(P) to a left adjoint functor from the category DCPO of dcpo's to the category CPAlg of C-prealgebraic lattices.
Description: This is the final draft, after peer-review, of a manuscript published in Commentationes mathematicae Universitatis Carolinae. The published version is available online at
ISSN: 0010-2628
Appears in Collections:Journal Articles

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