Representation theorems for directed completions of consistent algebraic L-domains |
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Authors: | Xuxin Mao Luoshan Xu |
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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 |
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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. |
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Keywords: | 06A11 06B35 54H10 |
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