Please use this identifier to cite or link to this item: http://hdl.handle.net/10497/15605
Title: 
Lattices of Scott-closed sets
Authors: 
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 http://cmuc.karlin.mff.cuni.cz/pdf/cmuc0902/hozhao.pdf
URI: 
ISSN: 
0010-2628
Appears in Collections:Journal Articles

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