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Representation theorems for directed completions of consistent algebraic L-domains
Authors:Xuxin Mao  Luoshan Xu
Institution:(1) Department of Mathematics, Nanjing University, Nanjing, 210093, Jiangsu, P.R. China;(2) Department of Mathematics, Yangzhou University, Yangzhou, 225002, Jiangsu, P.R. China
Abstract:In this paper, consistent algebraic L-domains are considered. One algebraic and two topological characterization theorems for their directed completions are given. It is proved that eliminating a set of maximal elements with empty interior from an algebraic L-domain results a consistent algebraic L-domain whose directed completion is just the given algebraic L-domain up to isomorphism. It is also proved that the category CALDOM of consistent algebraic L-domains and Scott continuous maps is Cartesian closed and has the category ALDOM of algebraic L-domains and Scott continuous maps as a full reflective subcategory. Received January 8, 2005; accepted in final form June 15, 2005.
Keywords:06A11  06B35  54H10
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