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中文摘要：
引入Domain子空间的概念,得到Scott开集和闭集都是Domain的子空间。证明连续Domain或代数Domain对开子空间和闭子空间都是可遗传的。证明连续Domain或代数Domain在保Waybelow序的Scott连续映射下保持不变。
英文摘要：
Firstly, the concepts of sub-dcpo and sub-space of a domain are given and both Scott open sets and Scott closed sets are proved to be sub-spaces. Then continuous domains or algebraic domains are hereditary for Scott open subsets and Scott closed subsets. Finally, it is proved that the image of continuous domain or algebraic domain under the waybelow-preserving Scott continuous maps is still continuous or algebraic.
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