Fundamental study: Dcpo-completion of posets
Fundamental study: Dcpo-completion of posets
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DOI：
10.1016/j.tcs.2010.02.020
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发表时间：
2010-05
影响因子：
1.1
通讯作者：
Dongsheng Zhao;T. Fan
中科院分区：
文献类型：
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作者：
Dongsheng Zhao;T. Fan
我们引入了偏序集的一种新的dcpo-完备化，称为D-完备化。对任意偏序集P，存在D-完备化，且P与它的D-完备化具有同构的Scott闭集格。这个完备化是幂等的。偏序集P是连续的（代数的）当且仅当它的D-完备化是连续的（代数的）。利用D-完备化，我们构造了偏序集的局部dcpo-完备化，它修正了Mislove给出的偏序集的局部dcpo-完备化。在最后一节中，我们定义并研究了有界清醒空间。
We introduce a new type of dcpo-completion of posets, called D-completion. For any poset P, the D-completion exists, and P and its D-completion have the isomorphic Scott closed set lattices. This completion is idempotent. A poset P is continuous (algebraic) if and only if its D-completion is continuous(algebraic). Using the D-completion, we construct the local dcpo-completion of posets, that revises the one given by Mislove. In the last section, we define and study bounded sober spaces.